Answer to Question #303232 in Statistics and Probability for MEHRAB

Question

indicate whether each of the following statements is true or false. if false indicate why.

a) if P(A/B) =0,then A and B are mutually exclusive.

b) if P(A/B) =0,then A and B are independent.

c) if P(A/B) = P(B/A), then P(A)=P(B).

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

Answer 1

a) For Mutually Exclusive events $P(A/B)=0$ is true since if event B has occurred event A cannot.

b) For Independent Events $P(A/B)=0$ is false since the probability of event A occurring does not depend on the probability of event B has occurred but still remains the probability of event A occurring.

c) P(A/B) = P(B/A) is true if and only if P(A)=P(B)

d)if A and B are independent, then P(A)=P(B) is false since the probability of each event is different and does not depend on the other.