Question

A and B are two events such that $P\left(A\right)=\frac{1}{2},P\left(B\right)=\frac{1}{3},P(A\cap B)=\frac{1}{4}$. Find $P\left(A|B\right)$.

• A. $\frac{3}{4}$
• B. $\frac{5}{7}$
• C. $\frac{1}{16}$
• D. $\frac{1}{18}$

Answer 1

The correct option is A $\frac{3}{4}$

$P\left(A\right)=\frac{1}{2},P\left(B\right)=\frac{1}{3},P(A\cap B)=\frac{1}{4}$

$P\left(A|B\right)=\frac{P(A\cap B)}{P\left(B\right)}$

$=\frac{1/4}{1/3}=\frac{3}{4}$