NCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.5

The topics and sub-topics included in Chapter 13 Probability the following:

Section Name	Topic Name
13	Probability
13.1	Introduction
13.2	Conditional Probability
13.3	Multiplication Theorem on Probability
13.4	Independent Events
13.5	Bayes’ Theorem
13.6	Random Variables and its Probability Distributions
13.7	Bernoulli Trials and Binomial Distribution

NCERT Solutions for Class 12 Maths Chapter 13 Probability 13.5 are part of NCERT Solutions for Class 12 Maths. Here we have given Class 12 Maths NCERT Solutions Probability 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:

Question 2.
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:

Question 3.
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability, of two successes.
Solution:

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?
(iii) none is spade?
Solution:

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:

Question 6.
A bag consists of 10 balls each marked with one of the digits 0 to 9. If four bails are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?
Solution:

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:

Question 8
Suppose X has a binomial distribution $B\left( 6,\frac { 1 }{ 2 } \right)$ . 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:

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:

Question 10.
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?
(a) at least once,
(b) exactly once,
(c) at least twice?
Solution:

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

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

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:

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) ${ \left( \frac { 1 }{ 2 } \right) }^{ 5 }$
(c) ${ \left( \frac { 9 }{ 10 } \right) }^{ 5 }$
(d) $\frac { 9 }{ 10 }$
Solution:

Question 15.
The probability that a student is not a swimmer is $\frac { 1 }{ 5 }$ . Then the probability that out of five students, four are swimmers is:

Solution: