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RD Sharma Solution CLass 12 Mathematics Chapter 33 Binomial Distribution

Chapter 33 – Binomial Distribution Exercise Ex. 33.1

Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8

Solution 8

Required Probability =

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Also, find the mean and variance of this distribution.

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

Solution 33

= 0.0256

Question 34

Solution 34

Question 35

Solution 35

Question 36

Solution 36

Question 37

Solution 37

Question 38

Solution 38

Question 39

Solution 39

Question 40

Solution 40

Question 41
Solution 41
Question 42

Solution 42

Question 43

Solution 43

Question 44

Solution 44

Question 45

Solution 45

Question 46

Solution 46

Question 47

Solution 47

Question 48
Solution 48
Question 49

Solution 49

Question 50

Find the probability that in 10 throws of a fair die a
score which is a multiple of 3 will be obtained in at least 8 of the throws.

Solution 50

Question 51

A die is thrown 5 times. Find the probability that an
odd number will come up exactly three times.

Solution 51

Question 52

The probability of a man hitting a target is 0.25. He
shoots 7 times. What is the probability of his hitting at least twice?

Solution 52

Question 53

A factory produces bulbs. The probability that one bulb is defective is  and they are packed in boxes of 10. From a single box, find the probability that

i. none of the bulbs is defective.

ii. exactly two bulls are defective.

iii. more than 8 bulbs work properly.

Solution 53

Note: Answer given in the book is incorrect.

Chapter 33 – Binomial Distribution Exercise Ex. 33.2

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20
Solution 20
Question 21
Solution 21
Question 22

From a lot of 15 bulbs which include 5 defective, sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of number of defective bulbs. Hence, find the mean of the distribution.

Solution 22

Out of 15 bulbs 5 are defective.

Question 23

A die is thrown three times. Let X be
the number of twos seen’. Find the expectation of X.

Solution 23

Question 24

A die is thrown twice. A ‘success’ is getting an even
number on a toss. Find the variance of number of successes.

Solution 24

Question 25

Three cards are drawn successively with replacement
from a well shuffled pack of 52 cards. Find the probability of the number
spades. Hence, find the mean of the distribution.

Solution 25

Chapter 33 – Binomial Distribution Exercise Ex. 33VSAQ

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

If for a binomial distribution p (x = 1) = p (x = 2) = , write p (x = 4) in terms of .

Solution 10

Chapter 33 – Binomial Distribution Exercise MCQ

Question 1

In a box containing 100 bulls, 10 are defective. What is the probability that out of a sample of 5 bulls , none is defective

Solution 1

Correct option: (a)

Question 2

Solution 2

Correct option: (b)

Question 3

A rifleman is firing at a distant target and has only 10% chance of hitting it. The least number of rounds, he must fire in order to have more than 50% chance of hitting it at least once is

a. 11

b. 9

c. 7

d. 5

Solution 3

Correct option: (c)

Question 4

A fair coin is tossed fixed number of times. If the probability of getting seven heads is equal to that of getting nine heads, the probability of getting two heads is

a. 15/28

b. 2/15

c. 15/213

d. none of these

Solution 4

Correct option: (c)

Question 5

A fair coin is tossed 100 times. The probability of getting tails an odd number of times is

a. 1/2

b. 1/8

c. 3/8

d. None of these

Solution 5

Correct option: (a)

Question 6

A fair die is thrown twenty times. The probability that on the tenth throw the fourth six appears is

Solution 6

Correct option: (c)

Question 7

a. 1/2

b. 1/3

c. 1/4

d. None of these

Solution 7

Correct option: (a)

Question 8

Let X denote the number of times heads occur in n tosses of a fair coin. If P (X = 4), P(X = 5) and P(X=6) are in AP; the value of n is

a. 7, 14

b. 10, 14

c. 12, 7

d. 14, 12

Solution 8

Correct option: (a)

Question 9

One hundred identical coins, each with probability p of showing heads are tossed once. If 0 < p

a. 1/2

b. 51/101

c. 49/101

d. None of these

Solution 9

Correct option: (b)

Question 10

A fair coin is tossed 99 times. If X is the number of times heads occur, then P (X = r) is maximum when r is

a. 49, 50

b. 50, 51

c. 51,52

d. None of these

Solution 10

Correct option: (a)

Question 11

The least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8, is

a. 7

b. 6

c. 5

d. 3

Solution 11

Correct option: (d)

Question 12

If the mean and variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than 1 is

a. 2/3

b. 4/5

c. 7/8

d. 15/16

Solution 12

Correct option: (d)

Question 13

A biased coin with probability p, 0< p

a. 1/3

b. 2/3

c. 2/5

d. 3/5

Solution 13

Correct option: (a)

Question 14

If X follows a binomial distribution with parameters n=8 and p=1/2, then p (|X-4|≤ 2) equals

Solution 14

Correct option: (b)

Question 15

If X follows a binomial distribution with parameters n=100 and p=1/3, then P(X=r) is maximum when r=

a. 32

b. 34

c. 33

d. 31

Solution 15

Correct option: (c)

Question 16

A fair die is tossed eight times. The probability that a third six is observed in the eight throw is

Solution 16

Correct option: (b)

Question 17

Fifteen coupons are numbered 1 to 15. Seven coupons are selected at random, one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9, is

Solution 17

Correct option: (d)

Question 18

A five-digit number is written down at random. The probability that the number is divisible by 5 and no two consecutive digits are identical, is

Solution 18

Correct option: (d)

NOTE: Answer not matching with back answer.

Question 19

A coin is tossed 10 times. The probability of getting exactly six heads is

Solution 19

Correct option: (b)

Question 20

The mean and variance of a binominal distribution are 4 and 3 respectively, then the probability of getting exactly six success in this distribution, is

Solution 20

Correct option: (b)

Question 21

In a binomial distribution, the probability of getting success is 1/4 and standard deviation is 3. Then, its mean is

a. 6

b. 8

c. 12

d. 10

Solution 21

Correct option: (c)

Question 22

A coin is tossed 4 times. The probability that at least one head turns up, is

Solution 22

Correct option: (d)

Question 23

For a binominal variate X, if n = 3 and P (X =1)= 8 P (X=3), then p =

a. 4/5

b. 1/5

c. 1/3

d. 2/3

Solution 23

NOTE: Answer not matching with back answer.

Question 24

A coin is tossed n times. The probability of getting at least once is greater than 0.8. Then, the least value of n, is

a. 2

b. 3

c. 4

d. 5

Solution 24

Correct option: (b)

Question 25

a. 5

b. 3

c. 10

d. 12

Solution 25

Correct option: (d)

Question 26

A box contains 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement at most one is defective?

Solution 26

Correct option: (d)

Question 27

Solution 27

Correct option: (a)

Question 28

The probability that a person is not a swimmer is 0.3. the probability that out of 5 persons 4 are swimmers is

Solution 28

Correct option: (a)

Question 29

Which one is not a requirement of a binomial distribution?

a. There are 2 outcomes for each trial

b. There is a fixed number of trials

c. The outcomes must be dependent on each other

d. The probability of success must be the same for all the trials.

Solution 29

Correct option: (c)

In Binomial distribution trails are independent.

Question 30

The probability of guessing correctly at least 8 out of 10 answer of a true false types examination is

Solution 30

Correct option: (b)

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