Question

A and B are two events such that P(A)=0.3,P(B)=0.4, and P(A∩B)=0.1. Calculate P(B|A) Give your answer as a fraction in its simplest form

Answer 1

The probability that event B happens given that event A happened first is calculated as follows:

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

Substituting with data:

$\begin{gathered} P(B|A)=\frac{0.1}{0.3} \\ P(B|A)=\frac{1}{3} \end{gathered}$