Question

A and B are events related to traffic lights. Given the probabilities: P(A) = 36%, P(B) = 25%, and P(A ∩ B) = 9%, what are A and B?

A) Independent events
B) Mutually exclusive events
C) Dependent events
D) Complementary events

Answer 1

Events A and B are independent because the given probability of their intersection, P(A AND B), is equal to the product of their individual probabilities.

Step-by-step explanation:

To determine whether events A and B are independent events, mutually exclusive events, dependent events, or complementary events, we must consider their definitions and the given probabilities. Independent events do not affect each other's occurrence whereas mutually exclusive events cannot occur at the same time.

Given that P(A) = 36%, P(B) = 25%, and P(A AND B) = 9%, we can check for independence. Two events are independent if P(A AND B) = P(A) × P(B). Calculating P(A)P(B) yields (0.36)(0.25) = 0.09, which is equal to the given P(A AND B). As the probabilities satisfy the condition for independent events, we conclude that events A and B are independent.