Question

2 In an experiment, the probability that event A occurs is and 1 the probability that event B occurs is 3 the probability that events A and B both occur is - 6 What is the probability that A occurs given that B occurs? Simplify any fractions.

Answer 1

Given the events A and B

The probability of A is P(A)=2/9

The probability of B is P(B)= 1/3

The probability of the intersection of both events, A and B is P(A∩B)= 1/6

You have to calculate the probability of A occurring, given that B already occurred, to do so you have to use the definition of the conditional probability:

$\begin{gathered} P(A|B)=\frac{P(A\cap B)}{P(B)} \\ P(A|B)=\frac{\frac{1}{6}}{\frac{1}{3}} \\ P(A|B)=\frac{1}{6}\cdot3 \\ P(A|B)=\frac{1}{2} \end{gathered}$

So, the probability of A, given that B occurred is 1/2