Chapter 33 : Binomial Distribution - Rd Sharma Solutions for Class 12-science Maths CBSE

Your CBSE Class 12 syllabus for Maths consists of topics such as linear programming, vector quantities, determinants, etc. which lay the foundation for further education in science, engineering, management, etc. Studying differential equations will be useful for exploring subjects such as Physics, Biology, Chemistry, etc. where your knowledge can be applied for scientific investigations.

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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 =4547 over 8192

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.

 

begin mathsize 12px style table attributes columnalign left end attributes row cell text Hence ,  the   probability   that   the   drawn   bulb   is   defective   is end text end cell row cell text P end text left parenthesis text Defective end text right parenthesis equals 5 over 15 equals 1 third end cell row cell text P end text left parenthesis text Not   defective end text right parenthesis equals 10 over 15 equals 2 over 3 end cell row cell text Let   X   denote   the   number   of   defective   bulbs   out   of   4. end text end cell row cell text Then ,  X   follows   binomial   distribution   with   end text end cell row cell straight n equals 4 comma text   end text straight p equals 1 third text   and   end text straight q equals 2 over 3 text   such   that end text end cell row cell straight P left parenthesis straight X equals straight r right parenthesis equals straight C presuperscript 4 subscript straight r open parentheses 1 third close parentheses to the power of straight r open parentheses 2 over 3 close parentheses to the power of 4 minus straight r end exponent semicolon straight r equals 0 comma 1 comma 2 comma 3 comma 4 end cell row cell text Mean end text equals sum from straight r equals 0 to 4 of rP left parenthesis straight r right parenthesis equals 1 cross times straight C presuperscript 4 subscript 1 open parentheses 1 third close parentheses open parentheses 2 over 3 close parentheses cubed plus 2 cross times straight C presuperscript 4 subscript 2 open parentheses 1 third close parentheses squared open parentheses 2 over 3 close parentheses squared end cell row cell plus 3 cross times straight C presuperscript 4 subscript 3 open parentheses 1 third close parentheses cubed open parentheses 2 over 3 close parentheses plus 4 cross times straight C presuperscript 4 subscript 4 open parentheses 1 third close parentheses to the power of 4 open parentheses 2 over 3 close parentheses to the power of 0 end cell row cell equals 32 over 81 plus 48 over 81 plus 24 over 81 plus 4 over 81 equals 108 over 81 equals 4 over 3 end cell end table end style

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 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

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)

  

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

rightwards double arrow q equals 0.4

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) = alpha, write p (x = 4) in terms of alpha.

Solution 10

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