Chapter 11.9, Problem 26E

To determine

To find the probability that event A occurs given that event B occurs

Answer to Problem 26E

the probability that event A occurs given that event B occursis $\frac{2}{5}$

Explanation of Solution

  $\begin{array}{l}\text{Let P be the possibility of both event A and B to occur}\\ \text{P(both A and B)= P(A)}\times \text{P(B given A)}\\ \frac{8}{100}=\frac{20}{100}\times \text{P(B given A)}\\ \text{P}\left(\text{B given A}\right)\text{ =}\frac{100\times 8}{20\times 100}\\ =\frac{2}{5}\end{array}$

Hence

  $\frac{2}{5}$ is the probability that event A occurs given that event B occurs