Question

A chorus has 50 girls and35 boys. If two are chosenat random to sing a duet,What is the probability thatboth will be boys?

Answer 1

The probability of an event is expressed as

`P(event)=\frac{number\text{ of desired outcome}}{number\text{ of possible outcome}}`

Given:

`\begin{gathered} number\text{ of boys = 35} \\ number\text{ of girls = 50} \\ total\text{ = 85} \end{gathered}`

This implies that the number of possible outcomes is 85.

Since two boys are chosen, the selection is thus without replacement.

The probability that the chosen two are boys is expressed as

`\begin{gathered} P(BB)=P(B)* P(B)\text{ without replacement} \\ =\frac{number\text{ of boys}}{total\text{ number}}*\frac{number\text{ of boys - 1}}{total\text{ number - 1}} \end{gathered}`

Thus, we have

`\begin{gathered} P(BB)=(35)/(85)*(35-1)/(85-1) \\ =(35)/(85)*(34)/(84) \\ =0.1667 \end{gathered}`

Hence, the probability that both will be boys is evaluated to be

`0.1667`