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

User Tim Banks
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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}

User Janavarro
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