Question

4 In an experiment, the probability that event B occurs is 5' and the probability that event A occurs given that event B occurs is 1. 3 What is the probability that events A and B both occur? Simplify any fractions. Submit

Answer 1

The probability that event B occurs is 4/5

`P(B)=(4)/(5)`

The probability that event A occurs given that event B occurs is 1/3

`P(A|B)=(1)/(3)`

What is the probability that events A and B both occur?

`P(A\: and\: B)=\text{?}`

Recall that the conditional probability is given by

`P(A|B)=(P(A\: and\: B))/(P(B))`

Re-writing the above formula for P(A and B)

`P(A\: and\: B)=P\mleft(A|B\mright)\cdot P(B)`

So, the probability that events A and B both occur is

`\begin{gathered} P(A\: and\: B)=P(A|B)\cdot P(B) \\ P(A\: and\: B)=(1)/(3)\cdot(4)/(5) \\ P(A\: and\: B)=(4)/(15) \end{gathered}`

Therefore, the probability that events A and B both occur is 4/15