Which of the following is not necessarily true for independent events A and B?
A) P(A and B) = P(A)P(B)
B) P(A|B)=P(A)
C) P(B|A)=P(B)
D) P(A or B) = P(A) + P(B)

Question

Quizplus · Accepted Answer

For independent events A and B, it's true that P(A and B) = P(A)P(B), P(A|B) = P(A), and P(B|A) = P(B). However, the formula for P(A or B) = P(A) + P(B) - P(A and B) is correct, not P(A or B) = P(A) + P(B) as stated in option D. This is because the intersection of A and B (the events happening together) needs to be subtracted to avoid double counting when A and B are not mutually exclusive.

Which of the Following Is Not Necessarily True for Independent