Question

and In an experiment, the probability that event A occurs is 3/5 the probability that event B occurs is 3/4 and the probability that events A and B occur is 3/7what is the probability that A occurs given that B occurs

Answer 1

$\begin{gathered} P(A)=\frac{3}{5} \\ P(B)=\frac{3}{4} \\ P(A\cap B)=\frac{3}{7} \\ P(A|B)=\text{?} \\ P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{\frac{3}{7}}{\frac{3}{4}}=\frac{3\cdot4}{3\cdot7}=\frac{4}{7} \\ P(A|B)=\frac{4}{7} \\ The\text{ probability that A occurs given B is }\frac{4}{7} \end{gathered}$