Question

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

Answer 1

We know that

• P(B) = 5/7.

,

• P(A | B) = 4/7.

We have to use the conditional probability formula

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

Replacing the given probabilities, we have

$\begin{gathered} \frac{4}{7}=\frac{P(B\cap A)}{\frac{5}{7}} \\ \frac{4}{7}\cdot\frac{5}{7}=P(B\cap A) \\ P(B\cap A)=\frac{20}{49} \end{gathered}$

Hence, the probability of A and B is 20/49.