Suppose P(A) = 0.4, P(B) = 0.3, and P(A B) = 0. Which one of the following statements correctly defines the relationship between events A and B?
A) Events A and B are independent, but not mutually exclusive.
B) Events A and B are mutually exclusive, but not independent.
C) Events A and B are neither mutually exclusive nor independent.
D) Events A and B are both mutually exclusive and independent.

Question

Suppose P(A) = 0.4, P(B) = 0.3, and P(A  B) = 0. Which one of the following statements correctly defines the relationship between events A and B?
A) Events A and B are independent, but not mutually exclusive. 
B) Events A and B are mutually exclusive, but not independent. 
C) Events A and B are neither mutually exclusive nor independent. 
D) Events A and B are both mutually exclusive and independent.

Quizplus · Accepted Answer

Since P(A 11eab386_b973_9248_aec0_531ab87bc0f5_TB4962_11 B) = 0, events A and B cannot occur at the same time, which means they are mutually exclusive. However, since P(A) = 0.4 and P(B) = 0.3, events A and B are not independent. Therefore, choice B is the correct answer.