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)=(P(B\cap A))/(P(B))`

Replacing the given probabilities, we have

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

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