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