Let A and B be two events in a sample space S such that P(A) = 0.5, P(B) = 0.5, and P(A ∩ B) = 0.24. Find the probabilities below.
(a) P(A|B)

(b) P(B|A)

Question

Let A and B be two events in a sample space S such that P(A) = 0.5, P(B) = 0.5, and P(A ∩ B) = 0.24. Find the probabilities below.
(a)    P(A|B)
  

(b)    P(B|A)

anonymous · Answer

Recall by definition that $P(\color{red}{A}\mid \color{blue}{B}) = \dfrac{P(\color{red}{A}\cap\color{blue}{B})}{P(\color{blue}{B})}$.  Hence, we can also say that $P(\color{blue}{B}\mid \color{red}{A}) = \dfrac{P(\color{red}{A}\cap\color{blue}{B})}{P(\color{red}{A})}$.

Do you think you can take things from here? :-)

anonymous · Answer

Yes! Thank you. .48 would be the answer to both