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.