# RD Sharma solutions for Class 12 Maths chapter 33 - Binomial Distribution [Latest edition]

## Chapter 33: Binomial Distribution

Exercise 33.1Exercise 33.Exercise 33.2Very Short AnswersMCQ
Exercise 33.1, Exercise 33. [Pages 12 - 15]

### RD Sharma solutions for Class 12 Maths Chapter 33 Binomial DistributionExercise 33.1, Exercise 33. [Pages 12 - 15]

Exercise 33.1 | Q 1 | Page 12

There are 6% defective items in a large bulk of items. Find the probability that a sample of 8 items will include not more than one defective item.

Exercise 33.1 | Q 2 | Page 13

A coin is tossed 5 times. What is the probability of getting at least 3 heads?

Exercise 33.1 | Q 3 | Page 13

A coin is tossed 5 times. What is the probability that tail appears an odd number of times?

Exercise 33.1 | Q 4 | Page 13

A pair of dice is thrown 6 times. If getting a total of 9 is considered a success, what is the probability of at least 5 successes?

Exercise 33.1 | Q 5.1 | Page 13

A fair coin is tossed 8 times, find the probability of exactly 5 heads  .

Exercise 33.1 | Q 5.2 | Page 13

A fair coin is tossed 8 times, find the probability of at least six heads

Exercise 33.1 | Q 5.3 | Page 13

A fair coin is tossed 8 times, find the probability of at most six heads.

Exercise 33.1 | Q 6 | Page 13

Find the probability of 4 turning up at least once in two tosses of a fair die.

Exercise 33.1 | Q 7 | Page 13

A coin is tossed 5 times. What is the probability that head appears an even number of times?

Exercise 33.1 | Q 8 | Page 13

The probability of a man hitting a target is 1/4. If he fires 7 times, what is the probability of his hitting the target at least twice?

Exercise 33.1 | Q 9 | Page 13

Assume that on an average one telephone number out of 15 called between 2 P.M. and 3 P.M. on week days is busy. What is the probability that if six randomly selected telephone numbers are called, at least 3 of them will be busy?

Exercise 33.1 | Q 10 | Page 13

If getting 5 or 6 in a throw of an unbiased die is a success and the random variable X denotes the number of successes in six throws of the die, find P (X ≥ 4).

Exercise 33.1 | Q 11 | Page 13

Eight coins are thrown simultaneously. Find the chance of obtaining at least six heads.

Exercise 33.1 | Q 12.1 | Page 13

Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that all the five cards are spades ?

Exercise 33.1 | Q 12.2 | Page 13

Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that  only 3 cards are spades ?

Exercise 33.1 | Q 12.3 | Page 13

Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that  none is a spade ?

Exercise 33.1 | Q 13.1 | Page 13

A bag contains 7 red, 5 white and 8 black balls. If four balls are drawn one by one with replacement, what is the probability that none is white ?

Exercise 33.1 | Q 13.2 | Page 13

A bag contains 7 red, 5 white and 8 black balls. If four balls are drawn one by one with replacement, what is the probability that all are white ?

Exercise 33.1 | Q 13.3 | Page 13

A bag contains 7 red, 5 white and 8 black balls. If four balls are drawn one by one with replacement, what is the probability that any two are white ?

Exercise 33.1 | Q 14 | Page 13

A box contains 100 tickets, each bearing one of the numbers from 1 to 100. If 5 tickets are drawn successively with replacement from the box, find the probability that all the tickets bear numbers divisible by 10.

Exercise 33.1 | Q 15 | Page 13

A bag contains 10 balls, each marked with one of the digits from 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?

Exercise 33.1 | Q 16 | Page 13

In a large bulk of items, 5 percent of the items are defective. What is the probability that a sample of 10 items will include not more than one defective item?

Exercise 33.1 | Q 17.1 | Page 13

The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs none will fuse after 150 days of use

Exercise 33.1 | Q 17.2 | Page 13

The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs not more than one will fuse after 150 days of use

Exercise 33.1 | Q 17.3 | Page 13

The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs more than one will fuse after 150 days of use

Exercise 33.1 | Q 17.4 | Page 13

The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs at least one will fuse after 150 days of use

Exercise 33.1 | Q 18 | Page 13

Suppose that 90% of people are right-handed. What is the probability that at most 6 of a random sample of 10 people are right-handed?

Exercise 33.1 | Q 19 | Page 13

A bag contains 7 green, 4 white and 5 red balls. If four balls are drawn one by one with replacement, what is the probability that one is red?

Exercise 33.1 | Q 20 | Page 13

A bag contains 2 white, 3 red and 4 blue balls. Two balls are drawn at random from the bag. If X denotes the number of white balls among the two balls drawn, describe the probability distribution of X.

Exercise 33.1 | Q 21 | Page 13

An urn contains four white and three red balls. Find the probability distribution of the number of red balls in three draws with replacement from the urn.

Exercise 33.1 | Q 22 | Page 13

Find the probability distribution of the number of doublets in 4 throws of a pair of dice.

Exercise 33.1 | Q 23 | Page 13

Find the probability distribution of the number of sixes in three tosses of a die.

Exercise 33.1 | Q 24 | Page 13

A coin is tossed 5 times. If X is the number of heads observed, find the probability distribution of X.

Exercise 33.1 | Q 25 | Page 13

An unbiased die is thrown twice. A success is getting a number greater than 4. Find the probability distribution of the number of successes.

Exercise 33.1 | Q 26 | Page 13

A man wins a rupee for head and loses a rupee for tail when a coin is tossed. Suppose that he tosses once and quits if he wins but tries once more if he loses on the first toss. Find the probability distribution of the number of rupees the man wins.

Exercise 33.1 | Q 27 | Page 13

Five dice are thrown simultaneously. If the occurrence of 3, 4 or 5 in a single die is considered a success, find the probability of at least 3 successes.

Exercise 33.1 | Q 28 | Page 14

The items produced by a company contain 10% defective items. Show that the probability of getting 2 defective items in a sample of 8 items is

$\frac{28 \times 9^6}{{10}^8} .$

Exercise 33.1 | Q 29 | Page 14

A card is drawn and replaced in an ordinary pack of 52 cards. How many times must a card be drawn so that (i) there is at least an even chance of drawing a heart (ii) the probability of drawing a heart is greater than 3/4?

Exercise 33.1 | Q 30 | Page 14

The mathematics department has 8 graduate assistants who are assigned to the same office. Each assistant is just as likely to study at home as in office. How many desks must there be in the office so that each assistant has a desk at least 90% of the time?

Exercise 33.1 | Q 31 | Page 14

An unbiased coin is tossed 8 times. Find, by using binomial distribution, the probability of getting at least 6 heads.

Exercise 33.1 | Q 32 | Page 14

Six coins are tossed simultaneously. Find the probability of getting

Exercise 33.1 | Q 33 | Page 14

Suppose that a radio tube inserted into a certain type of set has probability 0.2 of functioning more than 500 hours. If we test 4 tubes at random what is the probability that exactly three of these tubes function for more than 500 hours?

Exercise 33.1 | Q 34.1 | Page 14

The probability that a certain kind of component will survive a given shock test is $\frac{3}{4} .$  Find the probability that among 5 components tested exactly 2 will survive .

Exercise 33.1 | Q 34.2 | Page 14

The probability that a certain kind of component will survive a given shock test is $\frac{3}{4} .$  Find the probability that among 5 components tested at most 3 will survive .

Exercise 33.1 | Q 35.1 | Page 14

Assume that the probability that a bomb dropped from an aeroplane will strike a certain target is 0.2. If 6 bombs are dropped, find the probability that exactly 2 will strike the target .

Exercise 33.1 | Q 35.2 | Page 14

Assume that the probability that a bomb dropped from an aeroplane will strike a certain target is 0.2. If 6 bombs are dropped, find the probability that at least 2 will strike the target

Exercise 33.1 | Q 36.1 | Page 14

It is known that 60% of mice inoculated with a serum are protected from a certain disease. If 5 mice are inoculated, find the probability that none contract the disease .

Exercise 33.1 | Q 36.2 | Page 14

It is known that 60% of mice inoculated with a serum are protected from a certain disease. If 5 mice are inoculated, find the probability that more than 3 contract the disease .

Exercise 33.1 | Q 37 | Page 14

An experiment succeeds twice as often as it fails. Find the probability that in the next 6 trials there will be at least 4 successes.

Exercise 33.1 | Q 38 | Page 14

In a hospital, there are 20 kidney dialysis machines and the chance of any one of them to be out of service during a day is 0.02. Determine the probability that exactly 3 machines will be out of service on the same day.

Exercise 33.1 | Q 39.1 | Page 14

The probability that a student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university none will graduate

Exercise 33.1 | Q 39.2 | Page 14

The probability that a student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university only one will graduate .

Exercise 33. | Q 39.3 | Page 14

The probability that a student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university all will graduate .

Exercise 33.1 | Q 40 | Page 14

Ten eggs are drawn successively, with replacement, from a lot containing 10% defective eggs. Find the probability that there is at least one defective egg.

Exercise 33.1 | Q 41 | Page 14

In a 20-question true-false examination, suppose a student tosses a fair coin to determine his answer to each question. For every head, he answers 'true' and for every tail, he answers 'false'. Find the probability that he answers at least 12 questions correctly.

Exercise 33.1 | Q 42 | Page 15

Suppose X has a binomial distribution with = 6 and $p = \frac{1}{2} .$  Show that X = 3 is the most likely outcome.

Exercise 33.1 | Q 43 | Page 15

In a multiple-choice examination with three possible answers for each of the five questions out of which only one is correct, what is the probability that a candidate would get four or more correct answers just by guessing?

Exercise 33.1 | Q 44.1 | Page 15

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is $\frac{1}{100} .$  What is the probability that he will win a prize at least once.

Exercise 33.1 | Q 44.2 | Page 15

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is $\frac{1}{100} .$  What is the probability that he will win a prize exactly once.

Exercise 33.1 | Q 44.3 | Page 15

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is $\frac{1}{100} .$  What is the probability that he will win a prize at least twice.

Exercise 33.1 | Q 45 | Page 15

The probability of a shooter hitting a target is $\frac{3}{4} .$ How many minimum number of times must he/she fire so that the probability of hitting the target at least once is more than 0.99?

Exercise 33.1 | Q 46 | Page 15

How many times must a man toss a fair coin so that the probability of having at least one head is more than 90% ?

Exercise 33.1 | Q 47 | Page 15

How many times must a man toss a fair coin so that the probability of having at least one head is more than 80% ?

Exercise 33.1 | Q 48 | Page 15

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of the number of successes.

Exercise 33.1 | Q 49 | Page 15

From a lot of 30 bulbs that includes 6 defective bulbs, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.

Exercise 33.1 | Q 50 | Page 15

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.

Exercise 33.1 | Q 51 | Page 15

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

Exercise 33.1 | Q 52 | Page 15

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?

Exercise 33.1 | Q 53.1 | Page 15

A factory produces bulbs. The probability that one bulb is defective is $\frac{1}{50}$ and they are packed in boxes of 10. From a single box, find the probability that none of the bulbs is defective .

Exercise 33.1 | Q 53.2 | Page 15

A factory produces bulbs. The probability that one bulb is defective is $\frac{1}{50}$ and they are packed in boxes of 10. From a single box, find the probability that exactly two bulbs are defective

Exercise 33.1 | Q 53.3 | Page 15

A factory produces bulbs. The probability that one bulb is defective is $\frac{1}{50}$ and they are packed in boxes of 10. From a single box, find the probability that  more than 8 bulbs work properly

Exercise 33.1 | Q 54 | Page 15

A box has 20 pens of which 2 are defective. Calculate the probability that out of 5 pens drawn one by one with replacement, at most 2 are defective.

Exercise 33.2 [Pages 25 - 26]

### RD Sharma solutions for Class 12 Maths Chapter 33 Binomial DistributionExercise 33.2 [Pages 25 - 26]

Exercise 33.2 | Q 1 | Page 25

Can the mean of a binomial distribution be less than its variance?

Exercise 33.2 | Q 2 | Page 25

Determine the binomial distribution whose mean is 9 and variance 9/4.

Exercise 33.2 | Q 3 | Page 25

If the mean and variance of a binomial distribution are respectively 9 and 6, find the distribution.

Exercise 33.2 | Q 4 | Page 25

Find the binomial distribution when the sum of its mean and variance for 5 trials is 4.8.

Exercise 33.2 | Q 5 | Page 25

Determine the binomial distribution whose mean is 20 and variance 16.

Exercise 33.2 | Q 6 | Page 25

In a binomial distribution the sum and product of the mean and the variance are $\frac{25}{3}$ and $\frac{50}{3}$

respectively. Find the distribution.

Exercise 33.2 | Q 7 | Page 25

The mean of a binomial distribution is 20 and the standard deviation 4. Calculate the parameters of the binomial distribution.

Exercise 33.2 | Q 8 | Page 25

If the probability of a defective bolt is 0.1, find the (i) mean and (ii) standard deviation for the distribution of bolts in a total of 400 bolts.

Exercise 33.2 | Q 9 | Page 25

Find the binomial distribution whose mean is 5 and variance $\frac{10}{3} .$

Exercise 33.2 | Q 10 | Page 25

If on an average 9 ships out of 10 arrive safely at ports, find the mean and S.D. of the ships returning safely out of a total of 500 ships.

Exercise 33.2 | Q 11 | Page 25

The mean and variance of a binomial variate with parameters n and p are 16 and 8, respectively. Find P (X = 0), P (X = 1) and P (X ≥ 2).

Exercise 33.2 | Q 12 | Page 25

In eight throws of a die, 5 or 6 is considered a success. Find the mean number of successes and the standard deviation.

Exercise 33.2 | Q 13 | Page 25

Find the expected number of boys in a family with 8 children, assuming the sex distribution to be equally probable.

Exercise 33.2 | Q 14 | Page 25

The probability that an item produced by a factory is defective is 0.02. A shipment of 10,000 items is sent to its warehouse. Find the expected number of defective items and the standard deviation.

Exercise 33.2 | Q 15 | Page 25

A dice is thrown thrice. A success is 1 or 6 in a throw. Find the mean and variance of the number of successes.

Exercise 33.2 | Q 16 | Page 25

If a random variable X follows a binomial distribution with mean 3 and variance 3/2, find P (X ≤ 5).

Exercise 33.2 | Q 17 | Page 25

If X follows a binomial distribution with mean 4 and variance 2, find P (X ≥ 5).

Exercise 33.2 | Q 18 | Page 25

The mean and variance of a binomial distribution are $\frac{4}{3}$ and $\frac{8}{9}$ respectively. Find P (X ≥ 1).

Exercise 33.2 | Q 19 | Page 25

If the sum of the mean and variance of a binomial distribution for 6 trials is $\frac{10}{3},$  find the distribution.

Exercise 33.2 | Q 20 | Page 25

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of the number of successes and, hence, find its mean.

Exercise 33.2 | Q 21 | Page 25

Find the probability distribution of the number of doublets in three throws of a pair of dice and find its mean.

Exercise 33.2 | Q 22 | Page 25

From a lot of 15 bulbs which include 5 defective, a 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.

Exercise 33.2 | Q 23 | Page 25

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

Exercise 33.2 | Q 24 | Page 25

A die is tossed twice. A 'success' is getting an even number on a toss. Find the variance of number of successes.

Exercise 33.2 | Q 25 | Page 26

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

Exercise 33.2 | Q 26 | Page 26

An urn contains 3 white and 6 red balls. Four balls are drawn one by one with replacement from the urn. Find the probability distribution of the number of red balls drawn. Also find mean and variance of the distribution.

Exercise 33.2 | Q 27 | Page 26

Five bad oranges are accidently mixed with 20 good ones. If four oranges are drawn one by one successively with replacement, then find the probability distribution of number of bad oranges drawn. Hence find the mean and variance of the distribution.

### RD Sharma solutions for Class 12 Maths Chapter 33 Binomial DistributionVery Short Answers [Page 27]

Very Short Answers | Q 1 | Page 27

In a binomial distribution, if n = 20 and q = 0.75, then write its mean.

Very Short Answers | Q 2 | Page 27

If in a binomial distribution mean is 5 and variance is 4, write the number of trials.

Very Short Answers | Q 3 | Page 27

In a group of 200 items, if the probability of getting a defective item is 0.2, write the mean of the distribution.

Very Short Answers | Q 4 | Page 27

If the mean of a binomial distribution is 20 and its standard deviation is 4, find p.

Very Short Answers | Q 5 | Page 27

The mean of a binomial distribution is 10 and its standard deviation is 2; write the value of q.

Very Short Answers | Q 6 | Page 27

If the mean and variance of a random variable X with a binomial distribution are 4 and 2 respectively, find P (X = 1).

Very Short Answers | Q 7 | Page 27

If the mean and variance of a binomial variate X are 2 and 1 respectively, find P (X > 1).

Very Short Answers | Q 8 | Page 27

If in a binomial distribution n = 4 and P (X = 0) = $\frac{16}{81}$ , find q.

Very Short Answers | Q 9 | Page 27

If the mean and variance of a binomial distribution are 4 and 3, respectively, find the probability of no success.

Very Short Answers | Q 10 | Page 27

If for a binomial distribution P (X = 1) = P (X = 2) = α, write P (X = 4) in terms of α.

Very Short Answers | Q 11 | Page 27

An unbiased coin is tossed 4 times. Find the mean and variance of the number of heads obtained.

Very Short Answers | Q 12 | Page 27

If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9P(X = 3), then find the value of p.

MCQ [Pages 27 - 30]

### RD Sharma solutions for Class 12 Maths Chapter 33 Binomial DistributionMCQ [Pages 27 - 30]

MCQ | Q 1 | Page 27

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

•  $\left( \frac{9}{10} \right)^5$

•  $\frac{9}{10}$

•  10−5

•  $\left( \frac{1}{2} \right)^2$

MCQ | Q 2 | Page 28

If in a binomial distribution n = 4, P (X = 0) = $\frac{16}{81}$, then P (X = 4) equals

• $\frac{1}{16}$

• $\frac{1}{81}$

•  $\frac{1}{27}$

•  $\frac{1}{8}$

MCQ | Q 3 | Page 28

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

• 11

• 9

• 7

• 5

MCQ | Q 4 | Page 28

A fair coin is tossed a 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

• 15/28

• 2/15

• 15/213

• None of these

MCQ | Q 5 | Page 28

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

• 1/2

• 1/8

• 3/8

• None of these

MCQ | Q 6 | Page 28

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

• $\frac{ ^{20}{}{C}_{10} \times 5^6}{6^{20}}$

• $\frac{120 \times 5^7}{6^{10}}$

• $\frac{84 \times 5^6}{6^{10}}$

• None of these

MCQ | Q 7 | Page 28

If X is a binomial variate with parameters n and p, where 0 < p < 1 such that $\frac{P\left( X = r \right)}{P\left( X = n - r \right)}\text{ is }$ independent of n and r, then p equals

•  1/2

• 1/3

•  1/4

•  None of these

MCQ | Q 8 | Page 28

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

• 7, 14

• 10, 14

• 12, 7

• 14, 12

MCQ | Q 9 | Page 28

One hundred identical coins, each with probability p of showing heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of p is

• 1/2

• 51/101

• 49/101

• None of these

MCQ | Q 10 | Page 28

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

• 49, 50

• 50, 51

• 51, 52

• None of these

MCQ | Q 11 | Page 28

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

• 7

• 6

• 5

• 3

MCQ | Q 12 | Page 28

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

• 2/3

• 4/5

• 7/8

• 15/16

MCQ | Q 13 | Page 28

A biased coin with probability p, 0 < p < 1, of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is 2/5, then p equals

• 1/3

• 2/3

• 2/5

• 3/5

MCQ | Q 14 | Page 28

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

• $\frac{118}{128}$

• $\frac{119}{128}$

• $\frac{117}{128}$

• None Of these

MCQ | Q 15 | Page 28

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

• 32

• 34

• 33

• 31

MCQ | Q 16 | Page 29

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

• $\frac{^{7}{}{C}_2 \times 5^5}{6^7}$

• $\frac{^{7}{}{C}_2 \times 5^5}{6^8}$

• $\frac{^{7}{}{C}_2 \times 5^5}{6^6}$

• None of these

MCQ | Q 17 | Page 29

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

• $\left( \frac{3}{5} \right)^7$

• $\left( \frac{1}{15} \right)^7$

• $\left( \frac{8}{15} \right)^7$

• None of these

MCQ | Q 18 | Page 29

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

• $\frac{1}{5}$

• $\frac{1}{5} \left( \frac{9}{10} \right)^3$

• $\left( \frac{3}{5} \right)^4$

• None of these

MCQ | Q 19 | Page 29

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

• $\frac{512}{513}$

• $\frac{105}{512}$

• $\frac{100}{153}$

• $^{10}{}{C}_6$

MCQ | Q 20 | Page 29

If the mean and variance of a binomial distribution are 4 and 3, respectively, the probability of getting exactly six successes in this distribution is

• $^{16}{}{C}_6 \left( \frac{1}{4} \right)^{10} \left( \frac{3}{4} \right)^6$

• $^{16}{}{C}_6 \left( \frac{1}{4} \right)^6 \left( \frac{3}{4} \right)^{10}$

• $^{12}{}{C}_6 \left( \frac{1}{20} \right) \left( \frac{3}{4} \right)^6$

• $^{12}{}{C}_6 \left( \frac{1}{4} \right)^6 \left( \frac{3}{4} \right)^6$

MCQ | Q 21 | Page 29

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

• 6

• 8

• 12

• 10

MCQ | Q 22 | Page 29

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

• $\frac{1}{16}$

• $\frac{2}{16}$

• $\frac{14}{16}$

• $\frac{15}{16}$

MCQ | Q 23 | Page 29

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

• 4/5

• 1/5

• 1/3

• 2/3

• None of these

MCQ | Q 24 | Page 29

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

• 2

• 3

• 4

• 5

MCQ | Q 25 | Page 29

The probability of selecting a male or a female is same. If the probability that in an office of n persons (n − 1) males being selected is  $\frac{3}{2^{10}}$ , the value of n is

• 5

• 3

• 10

• 12

MCQ | Q 26 | Page 29

Mark the correct alternative in the following question:
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?

• $\left( \frac{9}{10} \right)^5$

• $\frac{1}{2} \left( \frac{9}{10} \right)^4$

• $\frac{1}{2} \left( \frac{9}{10} \right)^5$

• $\left( \frac{9}{10} \right)^5 + \frac{1}{2} \left( \frac{9}{10} \right)^4$

MCQ | Q 27 | Page 29

Mark the correct alternative in the following question:
Suppose a random variable X follows the binomial distribution with parameters n and p, where 0 < p < 1. If $\frac{P\left( X = r \right)}{P\left( X = n - r \right)}$ is independent of n and r, then p equals

• $\frac{1}{2}$

• $\frac{1}{3}$

• $\frac{1}{5}$

• $\frac{1}{7}$

MCQ | Q 28 | Page 30

Mark the correct alternative in the following question:
The probability that a person is not a swimmer is 0.3. The probability that out of 5 persons 4 are swimmers is

• $^{5}{}{C}_4 \left( 0 . 7 \right)^4 \left( 0 . 3 \right)$

• $^{5}{}{C}_1 \left( 0 . 7 \right) \left( 0 . 3 \right)^4$

• $^{5}{}{C}_4 \left( 0 . 7 \right) \left( 0 . 3 \right)^4$

• $\left( 0 . 7 \right)^4 \left( 0 . 3 \right)$

MCQ | Q 29 | Page 30

Mark the correct alternative in the following question:

Which one is not a requirement of a binomial dstribution?

• There are 2 outcomes for each trial

• There is a fixed number of trials

• The outcomes must be dependent on each other

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

MCQ | Q 30 | Page 30

Mark the correct alternative in the following question:

The probability of guessing correctly at least 8 out of 10 answers of a true false type examination is

• $\frac{7}{64}$

• $\frac{7}{128}$

• $\frac{45}{1024}$

• $\frac{7}{41}$

## Chapter 33: Binomial Distribution

Exercise 33.1Exercise 33.Exercise 33.2Very Short AnswersMCQ

## RD Sharma solutions for Class 12 Maths chapter 33 - Binomial Distribution

RD Sharma solutions for Class 12 Maths chapter 33 (Binomial Distribution) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 12 Maths solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 12 Maths chapter 33 Binomial Distribution are Variance of a Random Variable, Probability Examples and Solutions, Conditional Probability, Multiplication Theorem on Probability, Independent Events, Random Variables and Its Probability Distributions, Mean of a Random Variable, Bernoulli Trials and Binomial Distribution, Introduction of Probability, Properties of Conditional Probability, Bayes’ Theorem.

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