Question

Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P (E∩F) = 0.2, find P(E|F ) and P(F|E).

Answer 1

Given:
P(E) = 0.6
P(F) = 0.3
P(E∩F) = 0.2

∴ $P(E|F) = \frac {P(E∩F)}{P(F)}$ =$\frac {0.2}{0.3}$ =$\frac 23$

And, $P(F|E) =\frac {P(E∩F)}{P(E)}$ =$\frac {0.2}{0.6}$ =$\frac 13$