Question

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

Answer 1

Answer:

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

Step-by-step explanation:

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