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

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

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

Answer

Brief Explanations:

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

Answer:

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