Question

if events a and b are independent, what must be true? p(a|b) = p(b) p(a|b) = p(a) p(a) = p(b) p(a|b) = p(b|a)

Explanation:

The definition of independent events states that the occurrence of one event does not affect the probability of the occurrence of the other. The conditional - probability formula is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. For independent events $A$ and $B$, $P(A\cap B)=P(A)\times P(B)$. Substituting $P(A\cap B)=P(A)\times P(B)$ into the conditional - probability formula gives $P(A|B)=\frac{P(A)\times P(B)}{P(B)} = P(A)$.

Answer:

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