# NCERT Class 12-Mathematics: Chapter –13 Probability Part 5

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**Question 14:**

Let A and B be two events such that , and .

Then equals

(A)

(B)

(C)

(D)

**Answer:**

The correct answer is (C).

**Question 15:**

If A and B are independent events such that and , then which of the following is not correct?

(A) and are mutually exclusive

(B) and are independent

(C) and are independent

(D) and are independent

**Answer:**

The correct answer is (A)

**Question 16:**

Let be a discrete random variable. The probability distribution of is given below:

Then E (X) is equal to

(A)

(B)

(C)

(D)

**Answer:**

The correct answer is (B).

**Question 17:**

Let be a discrete random variable assuming values with probabilities , respectively. Then variance of is given by

(A)

(B)

(C)

(D)

**Answer:**

The correct answer is (C).

## Fill in the Blanks in Examples 18 and 19

**Question 18:**

If A and B are independent events such that and ___________

**Answer:**

**Question 19:**

If and are independent events then ________

**Answer:**

.

### State Whether Each of the Statement in Examples 20 to 22 is True or False

**Question 20:**

Let A and B be two independent events. Then

**Answer: False**

Because when events A and B are independent.

**Question 21:**

Three events A, B and C are said to be independent if .

**Answer:** **False**

Reason is that A, B, C will be independent if they are pairwise independent and .

**Question 22:**

One of the condition of Bernoulli trials is that the trials are independent of each other.

**Answer: True**