R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 15 Probability

Chapter 15 – Probability Exercise Ex. 15A

Question 1

Fill in the blanks:

(i) The
probability of an impossible event is ……. .

(ii) The
probability of a sure event is ……. .

(iii) For
any event E, P(E) + P(not E)= …… .

(iv) The
probability of a possible but not a sure event lies between …… and ……. .

(v) The
sum of probabilities of all the outcomes of an experiment is …….. .

Solution 1

(i) The probability of an
impossible event is zero.

(ii) The probability of a sure event is one.

(iii) For any event E, P(E) +
P(not E)= one .

(iv) The probability of a possible but not a sure event
lies between zero and one.

(v) The sum of probabilities of all the outcomes of an
experiment is one.

Question 2

A coin is tossed once. What is the
probability of getting a tail?

Solution 2

Question 3

Two
coins are tossed simultaneously. Find the probability of getting

(i) exactly

(ii) at

(iii) at

Solution 3

Question 4

A die is thrown once. Find the probability of getting:

(i)An even number

(ii)A number less than 5

(iii)A number greater than 2

(iv)A number between 3 and 6

(v)A number other than 3

(vi)The number 5

Solution 4

In a throw of a dice, all possible outcomes are 1, 2, 3, 4, 5, 6

Total number of possible outcomes = 6

(i)Let E be event of getting even number

Then, the favorable outcomes are 2, 4, 6

Number of favorable outcomes= 3

P(getting a even number)= P(E) =

(ii)Let R be the number less than 5

Then, the favorable outcomes are 1, 2, 3, 4

Number of favorable outcomes = 4

P(getting a number less than 5)= P(R) =

(iii)Let M be the event of getting a number greater than 2

Then, the favorable outcomes are 3, 4, 5, 6

Number of favorableoutcomes = 4

P(getting a number greater than 2)= P(M)

(iv)Let N be the number lying between 3 and 6

Then the favorable outcomes are 4, 5

Number of favorable outcomes = 2

P(getting a number 3 and 6)= P(N) =

(v)Let G be event of getting a number other than 3

Then the favorable outcomes are 1, 2, 4, 5, 6

Number of favorable outcomes = 5

P(getting a number other than 5)=P(G) =

(vi)Let T be event of getting a number 5

Then the favorable outcome is 5

Number of favorable outcomes = 1

P(getting a number 5)=P(T)

Question 5

A letter of English alphabet is chosen at
random. Determine the probability that the chosen letter is a consonant.

Solution 5

Question 6

Solution 6

Question 7

It is known that a box of 200 electric bulbs contains 16 defective bulbs. One bulb is taken out at random from the box. What is the probability that the bulb drawn is

(i)Defective

(ii)Non – defective?

Solution 7

Total number of bulbs = 200

Number of defective bulbs = 16

(i)Let be the event of getting a defective bulb

Total number of defective bulbs = 16

P(getting defective bulbs) = P() =

(ii)Let be the event of “getting non – defective bulb”

P(getting non defective bulb) =

Question 8

If
the probability of winning a game is 0.7, what is the probability of losing
it?

Solution 8

Question 9

There are 35 students in a class of whom 20 are boys
and 15 are girls. From these students one is chosen at random. What is the
probability that the chosen student is a (i) boy,
(ii) girl?

Solution 9

Question 10

In a lottery there are 10 prizes and 25
blanks. What is the probability of getting a prize?

Solution 10

Question 11

250 lottery tickets were sold and there are 5 prizes on these tickets. If Kunal has purchased one lottery ticket, what is the probability that he wins a prize?

Solution 11

Total number of tickets sold = 250

Number of prizes = 5

Let E be the event getting a prize

Number of favorable outcomes = 5

P(getting a prize) =

Question 12

17 cards numbered 1, 2, 3, 4, ….., 17 are put in a box and mixed thoroughly. A card is
drawn at random from the box. Find the probability that the card drawn bears
(i) an odd number (ii) a number divisible by 5.

Solution 12

Question 13

A game of chance consists of spinning an
arrow, which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6,
7, 8 and these are equally likely outcomes. Find the probability that the
arrow will point at any factor of 8.

Solution 13

Question 14

In a family of 3 children, find the
probability of having at least one boy.

Solution 14

Question 15

A bag contains 4 white balls, 5 red balls,
2 blacks balls and 4 green balls. A ball is drawn at
random from the bag. Find the probability that it is (i)
black, (ii) not green, (iii) red or white, (iv)
neither red nor green.

Solution 15

Question 16

A card is drawn at random from a well shuffled pack of 52 cards. Find the probability that the card drawn is neither a red card nor a queen.

Solution 16

There are 26 red cards containing a 2 queensand 2 more black queens are there in a pack of cards

P(getting a red card or a queen)

P(getting neither a red card nor a queen) =

Question 17

A card is drawn at random from a
well-shuffled pack of 52 cards. Find the probability of getting (i) a red king, (ii) a queen or a jack.

Solution 17

Question 18

A card is drawn from a well-shuffled pack
of 52 cards. Find the probability of getting (i) a
red face card (ii) a black king.

Solution 18

Question 19

Two different dice are tossed together. Find
the probability that (i) the number on each dice is
even, (ii) the sum of the numbers appearing on the two dice is 5.

Solution 19

Question 20

Two different dice are rolled
simultaneously. Find the probability that the sum of numbers in the two dice
is 10.

Solution 20

Question 21

When two dice are tossed together, find the
probability that the sum of numbers on their tops is less than 7.

Solution 21

Question 22

Two dice are rolled together. Find the
probability of getting such numbers on two dice whose product is a perfect
square.

Solution 22

Question 23

Two dice are rolled together. Find the
probability of getting such numbers on the two dice whose product is 12.

Solution 23

Question 24

Cards marked with numbers 5 to 50 are
placed in a box and mixed thoroughly. A card is drawn from the box at random.
Find the probability that the number on the number on the taken out card is (i) a prime number less than 10 (ii) a number which is a
perfect square.

Solution 24

Question 25

A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers 1, 2, 3,…. , 12 as shown in the figure. What is the probability that it will point to

(i)6?

(ii)An even number?

(iii)A prime number?

(iv)A number which is a multiple of 5?

Solution 25

Spinning arrow may come to rest at one of the 12 numbers

total number of outcomes = 12

(i)Probability that it will point at 6 =

(ii)Even numbers are 2, 4, 6, 8, 10 and 12. There are 6 numbers.

Probability that it points at even numbers =

(iii)The prime numbers are 2,3 5, 7 and 11. There are 5 prime numbers.

Probability that it points at prime number =

(iv)There are 2 numbers divisible by 5. These are 5 and 10.

Probability that a number is a multiple of 5 =

Question 26

12 defective pens are accidently mixed with
132 good ones. It is not possible to just look at pen and tell whether or not
it is defective. One pen is taken out is good one.

Solution 26

Question 27

A lot consists of 144 ballpoint pens of
which 20 are defective and others good. Tanvy will
buy a pen if it is good, but will not buy it if it is defective. The
shopkeeper draws one pen at random and gives it to her. What is the probability
that (i) she will buy it, (ii) she will not buy it?

Solution 27

Question 28

A box contains 90 discs which are numbered
from 1 to 90. If one disc is drawn at random from the box, find the
probability that it bears (i) a two-digit number,
(ii) a perfect square number, (iii) a number divisible by 5.

Solution 28

Question 29

(i) A lot of 20 bulbs contain 4 defective ones.
One bulb is drawn at random from the lot. What is the probability that this
bulb is defective?

(ii) Suppose the bulb drawn in (i) is not defective and not replaced. Now, bulb is drawn
at random from the rest. What is the probability that this bulb is not
defective?

Solution 29

Question 30

A bag contains lemon-flavoured
candies only. Hema takes out one candy without
looking into the bag. What is the probability that she takes out (i) an orange-flavoured candy?
(ii) a lemon-flavoured
candy?

Solution 30

Question 31

There are 40 students in a class of whom 25
are girls and 15 are boys. The class teacher has to select one student as a
class representative. He writes the name of each student on a separate card,
the cards being identical. Then the puts cards in a bag and stirs them
thoroughly. She then draws one card from the bag. What is the probability
that the name written on the card is the name of (i)
a girl? (ii) a boy?

Solution 31

Question 32

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing

(i)An ace

(iii)A ‘9’ of a black suit

(iv)A red king

Solution 32

Total number of all possible outcomes = 52

(i)P(getting an ace) =

(ii)P(getting a ‘4’ of spades) =

(iii)P(a ‘9’ of a black suit) =

(iv)P(getting a red king) =

Question 33

A card is drawn at random from a well- shuffled deck of 52 cards. Find the probability of getting

(i)A queen

(ii)A diamond

(iii)A king or an ace

(iv)A red ace

Solution 33

Total numbers of cards = 52

(i)There are 4 queen cards in a pack of cards

Probability of getting a queen card =

(ii)There are 13 cards of diamond in a pack of cards

probability ofgetting a diamond card =

(iii)In a pack of cards there are 4 kings and 4 aces

Number of such cards = 4 + 4 = 8

Probability of getting either a king or an ace =

(iv)There are two red aces in a pack of cards

probability of getting a red ace =

Question 34

One card is drawn from a well-shuffled deck
of 52 cards. Find the probability of getting

(i) a king of red suit

(ii) a face card

(iii) a red face card

(iv) a queen of black suit

(v) a jack of hearts

Solution 34

Question 35

A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is

(i)A card of spades or an ace

(ii)A red king

(iii)Either a king or a queen

(iv)Neither a king nor a queen

Solution 35

Total number of cards = 52

(i)There are 13 cards of spade (including 1 ace) and 3 more ace cards are there in a pack of cards

P(getting a card of spades or an ace) =

(ii)There are 2 red kings in a pack of cards

P(getting a red king) =

(iii)There are 4 kings and 4 queens in a pack of cards

P(getting either a king or a queen) =

(iv)P(getting neither a king nor a queen) =

Chapter 15 – Probability Exercise Ex. 15B

Question 1

A box contains 25 cards numbered from 1 to
25. A card is drawn at random from the bag. Find the probability that the
number on the drawn card is (i) divisible by 2 or
3, (ii) a prime number.

Solution 1

Question 2

A box contains cards numbered 3, 5, 7, 9, …., 35, 37. A card is drawn at random from the box. Find
the probability that the number on the card is a prime number.

Solution 2

Question 3

Cards numbered 1 to 30 are put in a bag. A card is
drawn at random from the bag. Find the probability that the number on the
drawn card is (i) not divisible by 3, (ii) a prime
number greater that 7, (iii) not a perfect square
number.

Solution 3

Question 4

Cards bearing numbers 1, 3, 5, …., 35 are kept in a bag. A card is drawn at random from
the bag. Find the probability of getting a card bearing (i)
a prime number less than 15, (ii) a number divisible by 3 and 5.

Solution 4

Question 5

A box contains cards bearing numbers 6 to
70. If one card is drawn at random from the box, Find the probability that it
bears (i) a one-digit number, (ii) a number
divisible by 5, (iii) an odd number less than 30, (iv) a composite number
between 50 and 70.

Solution 5

Question 6

Cards marked with numbers 1, 3, 5, ……, 101 are placed in a bag and mixed thoroughly. A card
is drawn at random from the bag. Find the probability that the number on the
drawn card is (i) less than 19, (ii) a prime number
less than 20.

Solution 6

Question 7

Tickets numbered 2, 3, 4, 5,.. , 100, 101 are placed in a box and mixed thoroughly. One ticket is drawn at random from the box. Find the probability that the number on the ticket is

(i)An even number

(ii)A number less than 16

(iii)A number which is a perfect square

(iv)A prime number less than 40

Solution 7

Total number of tickets = 100

(i)Even numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100

Total number of even number = 50

P(getting a even number) =

(ii)Numbers less than 16 are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15

Total number of numbers less than 16 is 14

P(getting a number less than 16) =

(iii)Numbers which are perfect square are 4, 9, 16, 25, 36, 49, 64, 81, 100

Total number of perfect squares = 9

P(getting a perfect square) =

(iv)Prime numbers less than 40 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37

Total number of prime numbers =12

P(getting a prime number less 40) =

Question 8

A
box contains 80 discs, which are numbered from 1 to 80. If one disc is drawn
at random from the box, find the probability that it bears a perfect square
number.

Solution 8

Question 9

A piggy bank contains
hundred 50-p coins, seventy Rs. 1 coin, fifty Rs. 2 coins and thirty Rs. 5
coins. If it equally likely that one of the coins will fall out when the bank
is turned upside down, what is the probability that the coin (i) will be a Rs. 1 coin? (ii) will
not be a Rs. 5 coins (iii) will be 50-p or a Rs. 2 coin?

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

A carton consists of 100 shirts of which 88
are good and 8 have minor defects. Rohit, a trader,
will only accept the shirts which are good. But, Kamal,
another trader, will only reject the shirts which have major defect. One
shirt is drawn at random from the carton. What is the probability that it is
acceptable to (i) Rohit,
(ii) Kamal?

Solution 14

Question 15

A group consists of 12 persons, of which 3
are extremely patient, other 6 are extremely honest and rest are extremely
kind. A person from the group is selected at random. Assuming that each
person is equally likely to be selected, find the probability of selecting a
person who is (i) extremely patient, (ii) extremely
kind or honest. Which of the above values you prefer more?

Solution 15

Question 16

Two dice are thrown simultaneously. What is the probability that

(i)5 will not come up on either of them

(ii)5 will not come up on at least one,

(iii)5 will come up at both the dice

Solution 16

Two dice are thrown simultaneously

Total number of outcomes = 6 6 = 36

(i)Favourable cases are: (1, 1), (1, 2), (1, 3), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 6) = 25.

Probability that 5 will not come upon either die

(ii)Favourable cases are: (1, 5), (2, 5), (3, 5), (4, 5), (5, 5), (6, 5), (5, 1), (5, 2), (5, 3), (5, 4), (5, 6) = 11

Probability that 5 will come at least once

(iii)5 will come up on both dice in 1 case = (5,5)

probability that 5 will come on both dice =

Question 17

Two dice are rolled once. Find the
probability of getting such numbers on two dice whose product is a perfect
square.

Solution 17

Question 18

A letter is chosen at random from the
letters of the word ‘ASSOCIATION’. Find the probability that the chosen
letter is a (i) vowel (ii) consonant (iii) an S.

Solution 18

Question 19

Five cards-the ten, jack, queen, king and
ace of diamonds are well shuffled with their faces downwards. One card is
then picked up at random. (a) What is the probability that the drawn card is
the queen?

(b) If the queen is drawn and put aside and
a second card is drawn, find the probability that the second card is (i) an ace, (ii) a queen.

Solution 19

Question 20

A card is drawn at random from a well
shuffled pack of 52 cards. Find the probability that the card drawn is
neither a red card nor a queen?

Solution 20

Question 21

What is the probability that an ordinary
year has 53 Mondays?

Solution 21

Question 22

All red face cards are removed from a pack
of playing cards. The remaining cards are well shuffled and then a card is
drawn at random from them. Find the probability that the drawn card is (i) a red card, (ii) a face card, (iii) a card of clubs.

Solution 22

Question 23

All kings, queens and aces are removed from
a pack of 52 cards. The remaining cards are well-shuffled and then a card is
drawn from it. Find the probability that the draw card is (i) a black face card, (ii) a red car

Solution 23

Question 24

A game consists of tossing a one-rupee coin
three times and noting its outcome each time. Find the probability of getting
(i) three heads, (ii) at least 2 tails.

Solution 24

Question 25

Find the probability that a leap year selected at
random will contain 53 Sundays.

Solution 25

Chapter 15 – Probability Exercise MCQ

Question 1

If P(E) denotes the probability of an event E then

(a) P(E)< 0

(b) P(E) > 1

(c) 0 P(E) 1

(d) -1 P(E) 1

Solution 1

Question 2

If the probability of occurrence of an event is p then the probability of non-happening of this event is

Solution 2

Question 3

What is the probability of an impossible event?

Solution 3

Question 4

What is the probability of a sure event?

Solution 4

Question 5

Which of the following cannot be the probability of an event?

Solution 5

Question 6

A number is selected at random from the numbers 1 to 30. What is the probability that the selected number is a prime number?

Solution 6

Question 7

The probability that a number selected at random from the numbers 1,2,3,….15 is a multiple of 4, is

Solution 7

Question 8

A box contains cards numbered 6 to 50.A card is drawn at random from the box. The probability that draw card has a number which is a perfect square is

Solution 8

Question 9

A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears prime number less than 23 is

Solution 9

Question 10

Cards bearing numbers 2, 3, 4…, 11 are kept in a bag. A card is drawn at random from the bag. The probability of getting a card with a prime number is

Solution 10

Question 11

One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number, which is a multiple of 7, is

Solution 11

Question 12

Which of the following cannot be the probability of an event?

Solution 12

Question 13

If the probability of winning a game is 0.4 then the probability of losing it, is

Solution 13

Question 14

If an event cannot occur then its probability is

Solution 14

Question 15

There are 20 tickets numbered as 1, 2, 3…., 20 respectively. One ticket is drawn at random. What is the probability that the number on the ticket drawn is a multiple of 5?

Solution 15

Question 16

There are 25 tickets numbered as 1, 2, 3, 4…., 25 respectively. One ticket is drawn at random. What is the probability that the number on the ticket drawn is a multiple of 3 or 5?

Solution 16

Question 17

Card, each market with one of the numbers 6, 7, 8, …, 15, are placed in a box and mixed thoroughly. One card is drawn at random from the box. What is the probability of getting a card with number less than 10?

Solution 17

Question 18

A die is thrown once. The probability of getting an even number is

Solution 18

Question 19

The probability of throwing a number greater than 2 with a fair die is

Solution 19

Question 20

A die is thrown once. The probability of getting an odd number greater than 3 is

Solution 20

Question 21

A die is thrown once. The probability of getting a prime number is

Solution 21

Question 22

Two dice are thrown together. The probability of getting the same number on both dice is

Solution 22

Question 23

The probability of getting 2 heads, when two coins are tossed, is

Solution 23

Question 24

Two dice are thrown together. The probability of getting a doublet is

Solution 24

Question 25

Two coins are tossed simultaneously. What is the probability of getting at most one head?

Solution 25

Question 26

Three coins are tossed simultaneously. What is the probability of getting exactly two heads?

Solution 26

Question 27

In a lottery, there are 8 prizes and 16 blanks. What is the probability of getting a prize?

Solution 27

Question 28

In a lottery, there are 6 prizes and 24 blacks. What is the probability of not getting a prize?

Solution 28

Question 29

A box contains 3 blue, 2 white and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will not be a white marble?

Solution 29

Question 30

A bag contains 4 red and 6 black balls. A ball is taken out of the bag at random. What is the probability of getting a black ball?

Solution 30

Question 31

A bag contains 8 red, 2 black and 5 white balls. One ball is drawn at random. What is the probability that the ball drawn is not black?

Solution 31

Question 32

A bag contains 3 white, 4 red and 5 black balls. One ball is drawn at random. What is the probability that the ball drawn is neither black nor white?

Solution 32

Question 33

A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of getting a black king?

Solution 33

Question 34

From a well-shuffled deck of 52 cards, one card is drawn at random. What is the probability of getting a queen?

Solution 34

Question 35

One card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of getting a face card?

Solution 35

Question 36

One card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of getting a black face card?

Solution 36

Question 37

One card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of getting a 6?

Solution 37

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