Question

Given the following: P(A)=0.28, P(B)=0.64, P(B|A)= 0.37, calculate P(A and B)

Answer 1

By definition of conditional probability you know that

`P(B|A)=(P(A\cap B))/(P(A))`

Now, replace the values that you have and solve for P(A and B)​

`\begin{gathered} P(B|A)=(P(A\cap B))/(P(A)) \\ 0.37=(P(A\cap B))/(0.28) \\ \text{ Multiply by 0.28 on both sides of the equation} \\ 0.37\cdot0.28=(P(A\cap B))/(0.28)\cdot0.28 \\ \text{ Therefore,} \\ 0.1036=P(A\cap B) \end{gathered}`