## Chapter 33 – Binomial Distribution Exercise Ex. 33.1

Required Probability =

Also, find the mean and variance of this distribution.

= 0.0256

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.

A die is thrown 5 times. Find the probability that an

odd number will come up exactly three times.

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?

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.

Note: Answer given in the book is incorrect.

## Chapter 33 – Binomial Distribution Exercise Ex. 33.2

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.

Out of 15 bulbs 5 are defective.

A die is thrown three times. Let X be‘

the number of twos seen’. Find the expectation of X.

A die is thrown twice. A ‘success’ is getting an even

number on a toss. Find the variance of number of successes.

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.

## Chapter 33 – Binomial Distribution Exercise Ex. 33VSAQ

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

## Chapter 33 – Binomial Distribution Exercise MCQ

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

Correct option: (a)

Correct option: (b)

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

Correct option: (c)

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. 15/2^{8}

b. 2/15

c. 15/2^{13}

d. none of these

Correct option: (c)

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

Correct option: (a)

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

Correct option: (c)

a. 1/2

b. 1/3

c. 1/4

d. None of these

Correct option: (a)

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

Correct option: (a)

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

Correct option: (b)

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

Correct option: (a)

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

Correct option: (d)

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

Correct option: (d)

A biased coin with probability p, 0< p

a. 1/3

b. 2/3

c. 2/5

d. 3/5

Correct option: (a)

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

Correct option: (b)

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

Correct option: (c)

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

Correct option: (b)

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

Correct option: (d)

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

Correct option: (d)

NOTE: Answer not matching with back answer.

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

Correct option: (b)

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

Correct option: (b)

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

Correct option: (c)

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

Correct option: (d)

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

NOTE: Answer not matching with back answer.

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

Correct option: (b)

a. 5

b. 3

c. 10

d. 12

Correct option: (d)

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?

Correct option: (d)

Correct option: (a)

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

Correct option: (a)

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.

Correct option: (c)

In Binomial distribution trails are independent.

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

Correct option: (b)