NCERT Solutions for Maths Class 12 Exercise 13.5

# NCERT Solutions for Maths Class 12 Exercise 13.5

## NCERT Solutions for Maths Class 12 Exercise 13.5

Hello Students. Welcome to maths-formula.com. In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 13.5.

You can download the PDF of NCERT Books Maths Chapter 10 for your easy reference while studying NCERT Solutions for Maths Class 12 Exercise 13.5.

Class 12th is a very crucial stage of your student’s life, since you take all important decisions about your career on this stage. Mathematics plays a vital role to take decision for your career because if you are good in mathematics, you can choose engineering and technology field as your career.

NCERT Solutions for Maths Class 12 Exercise 13.5 helps you to solve each and every problem with step by step explanation which makes you strong in mathematics.

All the schools affiliated with CBSE, follow the NCERT books for all subjects. You can check your syllabus from NCERT Syllabus for Mathematics Class 12.

NCERT Solutions for Maths Class 12 Exercise 13.5 are prepared by the experienced teachers of CBSE board. If you are preparing for JEE Mains and NEET level exams, then it will definitely make your foundation strong.

If you want to recall All Maths Formulas for Class 12, you can find it by clicking this link.

If you want to recall All Maths Formulas for Class 11, you can find it by clicking this link.

NCERT Solutions for Maths Class 12 Exercise 13.1

NCERT Solutions for Maths Class 12 Exercise 13.2

NCERT Solutions for Maths Class 12 Exercise 13.3

NCERT Solutions for Maths Class 12 Exercise 13.4

NCERT Solutions for Maths Class 12 Exercise 13.5

Maths Class 12 Ex 13.5 Question 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?

Solution:

There are 3 odd numbers on a die.
Probability of getting an odd number on a die = 3/6 = ½

Maths Class 12 Ex 13.5 Question 2.

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

Solution:

n(S) = 36, A = [(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}

Maths Class 12 Ex 13.5 Question 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?

Solution:

Probability of getting one defective item = 5% = 5/100 = 1/20
Probability of getting a good item = 1 – 1/20 = 19/20
A sample of 10 items include not more than one defective item.
Therefore, the sample contains at most one defective item.

Its probability = P (0) + P (1)

Maths Class 12 Ex 13.5 Question 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 spades?
(ii) only 3 cards are spades?

Solution:

S = {52 cards}, n(S) = 52
Let A denotes the favourable events.
A = {13 spades}, n(A)= 13

Maths Class 12 Ex 13.5 Question 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
(i) none
(ii) not more than one
(iii) more than one
(iv) at least one will fuse after 150 days of use

Solution:

Probability that a bulb gets fuse after 150 days of its use = 0.05
Probability that the bulb will not fuse after 150 days of its use = 1 – 0.05 = 0.95
(i) Probability that no bulb will fuse after 150

Maths Class 12 Ex 13.5 Question 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?

Solution:

S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, n(S) = 10
Let A represents that the ball is marked with the digit 0.
A = {0}, n(A) = 1

Maths Class 12 Ex 13.5 Question 7.

In an examination, 20 questions of true-false type are asked. Suppose a student tosses 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.

Solution:

Probability that student answers a question true = ½
That is, when a coin is thrown, the probability that a head is obtained = ½
Probability that his answer is false = 1 – ½ = ½
Probability that he answers at least 12 questions correctly = P(12) + P(13) + P(14) + …….. P(20)

Maths Class 12 Ex 13.5 Question 8.

Suppose X has a binomial distribution B(6, ½). Show that X = 3 is the most likely outcome.
(Hint: P(X = 3) is the maximum among all P(xi), xi = 0, 1, 2, 3, 4, 5, 6)

Solution:

Maths Class 12 Ex 13.5 Question 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?

Solution:

P = 1/3 and q = 1 – p = 1 – 1/3 = 2/3

Maths Class 12 Ex 13.5 Question 10.

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is 1/100. What is the probability that he will win a prize:
(a) at least once,
(b) exactly once,
(c) at least twice?

Solution:

Probability that the person wins the prize = 1/100
Probability of losing = 1 – 1/100 = 99/100
(a) Probability that he loses in all the lotteries

Maths Class 12 Ex 13.5 Question 11.

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

Solution:

S = {1, 2, 3, 4, 5, 6}, n(S) = 6
A = {5} i.e., n(A) = 1

Maths Class 12 Ex 13.5 Question 12.

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

Solution:

When a die is thrown, the probability of getting a six = 1/6
Probability of not getting a six = 1 – 1/6 = 5/6
Probability of getting at most 2 sixes in 6 throws of a single die = P(0) + P(1) + P(2)

Maths Class 12 Ex 13.5 Question 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?

Solution:

In each of the following, choose the correct answer:

Maths Class 12 Ex 13.5 Question 14.

In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is
(A) 10-1
(B) (½)5
(C) (9/10)5
(D) 9/10

Solution:

We have p = 1/10
Therefore, q = 1 – 1/10 = 9/10

For n = 5, r = 0, P(X = 0) = (9/10)5
Hence, the correct answer is option (C).

Maths Class 12 Ex 13.5 Question 15.

The probability that a student is not a swimmer is 1/5. Then the probability that out of five students, four are swimmers is:

Solution:

We have p = 4/5, therefore, q = 1 – 4/5 = 1/5,

For n = 5, r = 4

Hence, the correct answer is option (A).

1. 