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RD Sharma Solution CLass 12 Mathematics Chapter 31 Probability

Chapter 31 – Probability Exercise Ex. 31.1

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Chapter 31 – Probability Exercise Ex. 31.2

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 10

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 13

An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other without replacement. What is probability that both drawn balls are black?

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Chapter 31 – Probability Exercise Ex. 31.3

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 8

If A and B are two events such that

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 30

Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls? Given that

(i) the youngest is a girl

(ii) at least one is girl.

Solution 30

(i) Let ‘A’ be the event that both the children born are girls.

Let ‘B’ be the event that the youngest is a girl.

We have to find conditional probability P(A/B).

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

(ii) Let ‘A’ be the event that both the children born are girls.

Let ‘B’ be the event that at least one is a girl.

We have to find the conditional probability P(A/B).

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Chapter 31 – Probability Exercise Ex. 31.4

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 27

Given that the events ‘A coming in time’ and ‘B coming in time’ are independent.

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

The advantage of coming to school in time is that you will not miss any part of the lecture and will be able to learn more.

Question 28

Two dice are thrown together and the total score is
noted. The event E, F and G are “a total 4”, “a total of 9 or more”, and “a
total divisible by 5”, respectively. Calculate P (E), P(F)
and P(G) and decide which pairs of events, if any, are independent.

Solution 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 29

Let A and B be two independent events such that P (A) =
p1 and P (B) = p2. Describe in words the events whose
probabilities are:

(i) p1p2
(ii) (1 – p1)p2 (iii) 1-(1- p1) (1 – p2)
(iv) p1 + p2 = 2p1p2

Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Chapter 31 – Probability Exercise Ex. 31.5

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 35

In a hockey match, both teams A and B scored same number of goals upto the end of the game, so to decide the winner, the refree asked both the captains to throw a die alternately and decide that the team, whose captain gets a first six, will be declared the winner. If the captain of team A was asked to start, find their respective probabilities of winning the match and state whether the decision of the refree was fair or not.

Solution 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Chapter 31 – Probability Exercise Ex. 31.6

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 13

There machines E1, E2, E3
in a certain factory produce 50%, 25% and 25% respectively, of the total
daily output of electric bulbs. It is known that 4% of the tubes produced one
each of machines E1 and E2 are defective, and that 5%
of those produced on E3 are defective. If one tube is picked up at
random from a day’s production, calculate the probability that it is
defective.

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Chapter 31 – Probability Exercise Ex. 31.7

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 5

Suppose a girl throws a die. If she gets 1 or 2, she
tosses a coin three times and notes the number of tails. If she gets 3,4, 5
or 6, she tosses a coin once and notes whether a ‘head’ or ‘tail’ is
obtained. If she obtained exactly one ‘tail’, what is the probability that
she threw 3, 4, 5 or 6 with the die?

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Question 14

An item is manufactured by three machine A, B and C.
out of the total number of items manufactured during a specified period, 50%
are manufacture on machine A 30% on B and 20% on C. 2% of the items produced
on A and 2% of items produced on B are defective and 3% of these produced on
C are defective. All the items stored at one godown.
One items is drawn at random and is found to be
defective. What is the probability that it was manufactured on machine A?

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 15

There are three coins. One is two-headed coin (having head on both faces), another is biased coin that comes up heads 75% of the times and third is also a biased coin that comes up tail 40% of the times. One of the three coins is chosen at random and tossed, and it shows heads. What is the probability that it was the two-headed coin?

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 19

In a group of 400 people, 160 are smokers and non-vegetarian, 100 are smokers and vegetarian and the remaining are non-smokers and vegetarian. The probabilities of getting a special chest disease are 35%, 20% and 10% respectively. A person is chosen from the group at random and is found to be suffering from the disease. What is the probability that the selected person is a smoker and non-vegetarian?

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Chapter 31 – Probability Exercise Ex. 31VSAQ

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Chapter 31 – Probability Exercise MCQ

Question 1

If one ball is drawn at random from each of three boxes containing 3 white and 1 black, 2 white and black, 1 white and 3 black balls, then the probability that 2 white and 1 black balls will be draws is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 1

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 2

A and B draw two cards each, one after another, from a pack of well-shuffled pack of 52 cards. The probability that all the four cards drawn are of the same suit is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 2

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 3

A and B are two events such that P (A) = 0.25 and P (B) = 0.50. The probability of both happening together is 0.14. The probability of both A and B not happening is

a. 0.39

b. 0.25

c. 0.11

d. none of these

Solution 3

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 4

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 5

Indian play two matches each with West Indies and Australia. In any match the probabilities of India getting 0,1and 2 points are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is

a. 0.0875

b. 1/16

c. 0.1125

d. None of these

Solution 5

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 6

Three faces of an ordinary dice are yellow, two faces are red and one face is blue. The dice is rolled 3 times. The probability that yellow red and blue face appear in the first second and third throws respectively, is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 6

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 7

The probability that a leap year will have 53 Friday or 53 Saturday is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 7

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 8

A person writes 4 letters and addresses 4 envelopes. If the letters are placed in the envelopes at random, then the probability that all letters are not placed in the right envelopes, is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 8

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 9

A speaks truth in 75% cases and B speaks truth in 80% cases. Probability that they contradict each other in a statement, is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 9

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 10

Three integers are chosen at random from the first 20 integers. The probability that their product is even is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 10

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 11

Out of 30 consecutive integers, 2 are chosen at random. The probability that their sum is odd, is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 11

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 12

A bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected random wise, the probability that it is black or red ball is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 12

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 13

Two dice are thrown simultaneously. The probability of getting a pair of aces is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 13

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 14

An urn contains 9 balls two of which are red, three blue and four black. Three balls are drawn at random. The probability that they are of the same colour is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

Solution 14

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 15

A coin is tossed three times. If events A and B defined as A = Two heads come, B = Last should be head. Then , A and B are

a. independent

b. dependent

c. both

d. mutually exclusive

Solution 15

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 16

Five persons entered the life cabin on the ground floor  of an 8 floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floors beginning with the first, then probability of all 5 persons leaving different floor is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 16

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 17

A box contains 10 goods articles and 6 with defects. One item is drawn at random. The probability that it is either or has a defect is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 17

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 18

A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, the probability that it is rusted or is a nail is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

Solution 18

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 19

A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that these are of the same colour is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

Solution 19

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

a. 1/4

b. 1/2

c. 3/4

d. 3/8

Solution 20

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

Solution 21

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

a. 0.3

b. 0.5

c. 0.7

d. 0.9

Solution 22

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 23

A bag X contains 2 white and 3 black balls and another bag Y contains 4 white and 2 black balls. One bag is selected at random and a ball is drawn from it. Then, the probability chosen to be white is

a. 2/15

b. 7/15

c. 8/15

d. 14/15

Solution 23

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 24

Two persons A and B turn in throwing a pair of dice. The first person to throw 9 from both dice will be awarded the prize. If A throws first, then the probability that B wins the game is

a. 9/17

b. 8/17

c. 8/9

d. 1/9

Solution 24

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 25

The probability that in a year of 22nd century chosen at random, there will be 53 Sundays, is

a. 3/28

b. 2/28

c. 7/28

d. 5/28

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

NOTE: Answer not matching with back answer.

Question 26

From a set of 100 cards numbered 1 to 100, one card is draw at random. The probability that the number obtained on the card is divisible by 6 or 8 but not by 24 is

a. 6/25

b. 1/4

c. 1/6

d. 2/5

Solution 26

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

a. 1/10

b. 1/8

c. 7/8

d. 17/20

Solution 27

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

a. 14/17

b. 17/20

c. 7/8

d. 1/8

Solution 28

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 29

Associated to a random experiment two events A and B are such that P (B) = 3/5, P (A/B) = 1/2 and (A B) = 4/5. The Value of P(A) is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

Solution 29

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 30

If P(A) = 3/10, P(B) = 2/5 and P(A B) = 3/5, then P(A/B) + P(B/A) equals

a. 1/4

b. 7/2

c. 5/12

d. 1/3

Solution 30

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Note: option is modified.

Question 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

a. 5/9

b. 4/9

c. 4/13

d. 6/13

Solution 31

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 32

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 33

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 34

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 35

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 36

If P(A) = 0.4, P(B) = 0.8 and P(B/A)=0.6, then

 P(A B)=

a. 0.24

b. 0.3

c. 0.48

d. 0.96

Solution 36

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 37

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 38

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 39

If A and B are two events such that A ϕ, B = ϕ, then

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

Solution 39

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

Solution 40

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 41

If the events A and B are independent, then P(A B) is equal to

a. P(A) + P(B)

b. P(A) – P(B)

c. P(A) P(B)

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 41

Correct option: (c)

P(A B)= P(A) P(B) for independent events.

Question 42

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

Solution 42

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 43

If A and B are two independent events such that P(A) = 0.3, P(A B) = 0.5, then P(A/B) – P(B/A) =

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

Solution 43

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 44

A flash light has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, the probability that both are dead is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

Solution 44

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 45

A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement, then the probability of getting exactly one red ball is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

Solution 45

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 46

A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement, then the probability that exactly two of the three balls were red, the first ball being red, is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

Solution 46

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 47

In a college 30% students fail in physics, 25% fails in Mathematics and 10% fail in both. One student is chosen at random. The probability that she fails in Physics if she has failed in Mathematics in

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

Solution 47

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 48

Three persons A, B and C fire a target in turn starting with A. their probabilities of hitting the target are 0.4, 0.3 and 0.2 respectively. The probability of two hits is

a. 0.024

b. 0.452

c. 0.336

d. 0.138

Solution 48

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

NOTE: Answer not matching with back answer.

Question 49

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 49

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 50

Two cards are drawn from a well shuffled deck of 52 playing cards with replacement. The probability that both cards are queen is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 50

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 51

A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing 2 green balls and one blue ball is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 51

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 52

If two events are independent, then

a. they must be mutually exclusive

b. the sum of their probabilities must be equal to 1

c. (a) and (b) both are correct

d. none of the above is correct

Solution 52

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 53

Two dice are thrown. If it is known that the sum of the numbers on the dice was less than 6, the probability of getting a sum 3, is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

Solution 53

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 54

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 54

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

Question 55

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Solution 55

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 56

A die is thrown and a card is selected at random from a deck of 52 playing cards. The probability of getting an even number of the die and a spade card is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

Solution 56

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 57

Assume that in a family, each child is equally likely to be a boy or a girl. A family with three children is chosen at random. The probability that the eldest child is a girl given that the family has at least one girl is

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

Solution 57

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 58

Let A and B be two events. If P(A) = 0.2, P(B) = 0.4,

P(A B) = 0.6, then P(A/B) is equal to

a. 0.8

b. 0.5

c. 0.3

d. 0

Solution 58

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

Question 59

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability 

Solution 59

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Probability

NOTE: Answer not matching with back answer.

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