Chapter 5.3, Problem 80E

To determine

To find: The probability that all three females are selected

Answer to Problem 80E

The probability is 0.281.

Explanation of Solution

Given:

Number of males = 10

Number of females = 20

Number of students being selected = 3

Calculation:

The probability that all three females are selected can be calculated as:

  $\begin{array}{c}P\left(\text{Three females are selected}\right)=\frac{{}^{20}{C}_3}{{}^{30}{C}_3}\\ =\frac{\frac{20!}{\left(20-3\right)!\times 3!}}{\frac{30!}{\left(30-3\right)!\times 3!}}\\ =\frac{1140}{4060}\\ =0.281\end{array}$

The required probability is 0.281.