NCERT Solutions class 12 Maths Exercise 13.5

NCERT Solutions class 12 Maths Exercise 13.5 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Maths chapter wise NCERT solution for Maths part 1 and Maths part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

Download NCERT solutions for Probability as PDF.

NCERT Solutions class 12 Maths Probability

1.  A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of:

(i)  5 successes?

(ii)  at least 5 successes?

(iii)  at most 5 successes?

Ans.  S = {1, 2, 3, 4, 5, 6}    = 6

A = {1, 3, 5}       = 3

 =  and 

   = 6 and P (X = ) = C

(i) 

P (X = 5) = C (6, 5)  =

(ii) 

P (at least 5 success) = P (X = 5) + P (X = 6) =

(iii)  P (at most 5 success) = 1 – P (X = 6) =

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

Ans.   = 36, A = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}    = 6

 =  and 

   = 4 and  = 2

P (X = ) = C

P (X = 2) = C (4, 2)  =

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3.  There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?

Ans.   and

 = 10,  = 0, 1

P (not more than one defective items) = P (X = 0) + P (X = 1)

  = C (10, 0)  + C (10, 1)

  =

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NCERT Solutions class 12 Maths Exercise 13.5

4.  Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that:

(i)  all the five cards are spade?

(ii)  only 3 cards are spades?

(iii)  none is spade?

Ans.  S = 52 cards    = 52 and A = {13 spades}     13

 and

(i)   = 5,  = 5

P (X = ) =

P (X = 5) =

(ii)   = 5,  = 0

P (X = 3) =

(iii)   = 5,  = 0

P (X = 0) =

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NCERT Solutions class 12 Maths Exercise 13.5

5.  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.

Ans.   = 0.05 and  = 1 – 0.05 = 0.96

 = 5 and P (X = ) = C

(i)   = 0

P (X = 0) = C (5, 0),

(ii)  Not more than one success

P (not more than one success) = P (X = 0) + P (X = 1)

  =

  =

  =

  =

(iii)  P (more than one success) = 1 – [P (X = 0) + P (X = 1)]

=

(iv)  P (at least one success) = 1 – P (X = 0)

=

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NCERT Solutions class 12 Maths Exercise 13.5

6.  A bag consists of 10 balls each marked with one of the digits 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?

Ans.  S = {0, 1, 2 3, 4, 5, 6, 7, 8, 9}    = 10

Let A represents that the ball is marked with the digit 0.

 A = {0}     = 1

 and

   and P (X = ) =

Now P (one is marked with its digit 0) =

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NCERT Solutions class 12 Maths Exercise 13.5

7.  In an examination, 20 questions of true-false are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers ‘true’, if it falls tails, he answers ‘false’. Find the probability that he answers at least 12 questions correctly.

Ans.  S = {H, T}    = 2

Let A represents a head.

 A = {H}     = 1

 and

  and  P (X = ) =

P (at least 12 success) = P (X = 12) + P (X = 13) + ……… P (X = 20)

=

=

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NCERT Solutions class 12 Maths Exercise 13.5

8.  Suppose X has a binomial distribution B. Show that X = 3 is the most likely outcome.

Ans.  B      

 = 0, 1, 2, 3, 4, 5, 6

P (X = ) = C

Since 

Therefore, P (X = ) = C

Now,  out of C (6, 0), C (6, 1), C (6, 2), C (6, 3), C (6, 4), C (6, 5), C (6, 6), here C (6, 3) is maximum.

 P (X = 3) = C (6, 3)  =  =

Therefore, P (X = 3) is maximum, i.e.,

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NCERT Solutions class 12 Maths Exercise 13.5

9.  On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

Ans.   and

 and P (X = ) =

P (Four or more success) = P (X = 4) + P (X = 5)

= =  =

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NCERT Solutions class 12 Maths Exercise 13.5

10.  A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is   What is the probability that he will win a prize:

(a) at least once 

(b) exactly once 

(c) at least twice?

Ans.   and

(a)  P (at least one prize) = 1 – P (X = 0) =

(b)  P (exactly one prize) = P (X = 1) =

(c)  P (at least twice) = 1 – [P (X = 0) + P (X = 1)] =

=

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NCERT Solutions class 12 Maths Exercise 13.5

11.  Find the probability of getting 5 exactly twice in 7 throws of a die.

Ans.  S = {1, 2, 3, 4, 5, 6}    = 6

A = {5}       = 1

 and

 and P (X = ) =

P (X = 2) =

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NCERT Solutions class 12 Maths Exercise 13.5

12.  Find the probability of throwing at most 2 sixes in 6 throws of a single die.

Ans.  S = {1, 2, 3, 4, 5, 6}    = 6

Let A represents the favourable event i.e., 6

A = {6}     = 1

 and

 and P (X = ) =

P (X = 0) =

P (X = 1) =

P (X = 2) =

P (at most 2 success) = P (X = 0) + P (X = 1) + P (X = 2)

=  +  +

=   =

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NCERT Solutions class 12 Maths Exercise 13.5

13.  It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles 9 are defective?

Ans.   and

 and P (X = ) =

P (X = 9) =  =

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NCERT Solutions class 12 Maths Exercise 13.5

In each of the following, choose the correct answer:

14.  Binomial distribution is given this name because:

(A)  This distribution was evolved by James binomial.

(B)  Each trial has only two outcomes. Namely success and failure.

(C)  Its probability function is obtained by general of binomial expansion.

(D)  It is obtained by combining two distributions.

Ans.   and

P (X = 0) =

Therefore, option (C) is correct.

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NCERT Solutions class 12 Maths Exercise 13.5

15.  In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is:

(A)    

(B)    

(C)    

(D)  

Ans.   and

P (X = 4) =

Therefore, option (A) is correct.

NCERT Solutions class 12 Maths Exercise 13.5

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