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

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