Given P(A) = 0.45, P(B) = 0.30, P(A and B) = 0.05. Which of the following is true?
A) A and B are independent.
B) A and B are mutually exclusive.
C) A and B are collectively exhaustive.
D) A and B are not independent.
E) A and B are complimentary.

Question

Quizplus · Accepted Answer

If A and B were independent, then P(A and B) would be equal to P(A) × P(B) = 0.45 × 0.30 = 0.135. However, P(A and B) is given as 0.05, which is not equal to 0.135, so A and B are not independent. They are also not mutually exclusive because P(A and B) is not equal to 0. They are not collectively exhaustive or complementary either, as they do not cover all possibilities or add up to 1. Therefore, the only true statement is that A and B are not independent, so the answer is D.