**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**.

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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.

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**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?

(iii) none is spade?

**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(x_{i}), x_{i} = 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

Very good explanation. You can also read NCERT Solution for Maths Class 10

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