Question

select the correct answer. the probability of event a is x, and the probability of event b is y. if the two events are independent, which condition must be true? a. p(b|a)=y b. p(a|b)=y c. p(b|a)=x d. p(a|b)=x

Explanation:

Step1: Recall the definition of independent events

For two independent events A and B, the conditional - probability formula is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Since A and B are independent, $P(A\cap B)=P(A)\times P(B)$. Then $P(A|B)=\frac{P(A)\times P(B)}{P(B)} = P(A)$. Also, $P(B|A)=\frac{P(A\cap B)}{P(A)}=\frac{P(A)\times P(B)}{P(A)} = P(B)$.
If $P(A) = x$ and $P(B)=y$, then $P(A|B)=x$ and $P(B|A)=y$.

Answer:

C. $P(B|A)=y$