Question

Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted.

Answer 1

This is a conditional probability problem.

Let A be the event that the person is over 40

Let B be the event that the person is a root beer drinker

Probability of A given B is given by the equation:

`P(A\text{/B)=}(P(AnB))/(P(B))`
`\begin{gathered} P(\text{AnB)}=\frac{AnB}{Total\text{ number of subjects}} \\ P(\text{AnB)}=(30)/(255) \\ P(B)=\frac{number\text{ of root b}eer\text{ drinker}}{\text{Total number of subjects}} \\ P(B)=(25+20+30)/(255) \\ P(B)=(75)/(255) \end{gathered}`

Thus,

`\begin{gathered} P(A\text{/B)=}(30)/(255)/(75)/(255) \\ P(A\text{/B)=}(30)/(255)*(255)/(75) \\ P(A\text{/B)=}(30)/(75) \\ P(A\text{/B)=}(2)/(5) \end{gathered}`

Hence , the correct option is option B