# Given the following: P(A) = 0.3, P(B) = 0.2, P(A OR B) = 0.5, P(A AND B) = 0.

Which of the following is true?

A and B are disjoint.

A and B are neither disjoint nor independent.

A and B are independent.

A and B are disjoint and independent.

**Solution:**

Given:

**P(A) = 0.3, P(B) = 0.2, P(A or B) = 0.5, P(A and B) = 0**

Two events are disjoint if the events cannot occur at the same time.

**P(A and B) = 0, the events A and B cannot occur at the same time.**

So the events A and B are disjoint.

**Two events are said to be independent if the occurrence of one event does not affect the occurrence of the other.**

P(A and B) = P(A).P(B)

= P(A).P(B)

= 0.3 × 0.2

P(A and B) = 0.06

As 0.06 ≠ 0, the events A and B are not independent.

**Therefore, A and B are disjoint.**

## Given the following: P(A) = 0.3, P(B) = 0.2, P(A OR B) = 0.5, P(A AND B) = 0.

Which of the following is true?

**Summary:**

If P(A) = 0.3, P(B) = 0.2, P(A or B) = 0.5, P(A and B) = 0. A and B are disjoint is true.