Problem 23STE

Let A and B be events having positive probability. State whether each of the following statements is (i) necessarily true, (ii) necessarily false, or (iii) possibly true.

(a) If A and B are mutually exclusive, then they are independent.

(b) If A and B are independent, then they are mutually exclusive.

(c) P(A) = F(B) = .6, and A and B are mutually exclusive.

(d) P(A) = P(B) = .6, and A and B are independent.

Solution:

Step 1 of 5:

Let A and B are events with positive probability.

We have to find the given statements are (i) necessarily true, (ii) necessarily false, or (iii) possibly true.

- If A and B are mutually exclusive, then they are independent.
- If A and B are independent, then they are mutually exclusive.
- P(A), PB) = 0.6, then A and B are mutually exclusive.
- P(A), P(B) = 0.6, and A and B are independent.