Question

2 In an experiment, the probability that event B occurs is and the probability that event A occurs given 7 기 1 that event B occurs is = 4 What is the probability that events A and B both occur? Simplify any fractions.

Answer 1

`\begin{gathered} P(B)=(2)/(7) \\ P(A|B)=(1)/(4) \\ P(A\cap B)=\text{?} \\ \\ P(A|B)=(P(A\cap B))/(P(B)) \\ SOLVING\text{ }P(A\cap B) \\ P(A\cap B)=P(B)\cdot P(A|B) \\ \\ P(A\cap B)=(2)/(7)\cdot(1)/(4)=(2\cdot1)/(7\cdot4)=(2)/(28)=(1)/(14) \end{gathered}`