Chapter 13.3, Problem 32E

To determine

To find: The odds of no one has brown eyes.

Answer to Problem 32E

The odds of no one has brown eyesis $\frac{28}{197}$ .

Explanation of Solution

The probability of the successful outcome of an event is given by,

  $P\left(s\right)=\frac{s}{s+f}$

The probability of no one has brown eyes iscalculated as,

  $\begin{array}{c}P\left(\text{s}\right)=\frac{C\left(14,3\right)}{C\left(27,3\right)}\\ =\frac{364}{2925}\\ =\frac{28}{225}\end{array}$

The probability of failure is calculated as,

  $\begin{array}{c}P\left(f\right)=1-P\left(s\right)\\ =1-\frac{28}{225}\\ =\frac{197}{225}\end{array}$

The odds of no one has brown eyesis calculated as,

  $\begin{array}{c}\text{Odds}=\frac{P\left(s\right)}{P\left(f\right)}\\ =\frac{28/225}{197/225}\\ =\frac{28}{197}\end{array}$

Therefore, the odds ofno one has brown eyes is $\frac{28}{197}$ .