# NCERT Class 12-Mathematics: Chapter – 13 Probability Part 16 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 54**:

A die is tossed twice. A ‘success’ is getting an even number on a toss. Find the variance of the number of successes.

**Answer**:

Let be the random variable for a ‘success’ for getting an even number on a toss

At

At

At

Thus,

And

**Question 55**:

There are cards numbered to , one number on one card. Two cards are drawn at random without replacement. Let denote the sum of the numbers on two cards drawn. Find the mean and variance of .

**Answer**:

Here,

Let random variable be which denotes the sum of the numbers on two cards drawn.

At

At

At

At

At

At

Also,

## Objective Type Questions

### Choose the Correct Answer from the Given Four Options in Each of the Exercises from 56 to 82

**Question 56**:

If then is equal to

(A)

(B)

(C)

(D)

**Answer: (C)**

**Question 57**:

If equals

(A)

(B)

(C)

(D)

**Answer: (A)**

**Question 58**:

If and then equals

(A)

(B)

(C)

(D)

**Answer: (D)**