Question

P(A|B)=0.55 and P(B)=0.3, what is P(A^B)?

Answer 1

`\large\boxed{P(A\cap B)=0.165}`

Explanation:

`\text{We know:}\ P(A|B)=(P(A\cap B))/(P(B)).\\\\\text{We have}\ P(A|B)=0.55\ \text{and}\ P(B)=0.3.\\\\\text{Substitute:}\\\\0.55=(P(A\cap B))/(0.3)\qquad\text{multiply both sides by 0.3}\\\\(0.3)(0.55)=0.3\!\!\!\!\!\diagup^1\cdot(P(A\cap B))/(0.3\!\!\!\!\!\diagup_1)\\\\P(A\cap B)=0.165`