Chapter 13.3, Problem 30E

To determine

To find: The odds of all three students have blue eyes..

Answer to Problem 30E

The odds of all three students have blue eyes is $\frac{11}{184}$ .

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 all three students have blue eyes is calculated as,

  $\begin{array}{c}P\left(\text{s}\right)=\frac{C\left(11,3\right)}{C\left(27,3\right)}\\ =\frac{165}{2925}\\ =\frac{11}{195}\end{array}$

The probability of failure is calculated as,

  $\begin{array}{c}P\left(f\right)=1-P\left(s\right)\\ =1-\frac{11}{195}\\ =\frac{184}{195}\end{array}$

The odds of all three students have blue eyesis calculated as,

  $\begin{array}{c}\text{Odds}=\frac{P\left(s\right)}{P\left(f\right)}\\ =\frac{11/195}{184/195}\\ =\frac{11}{184}\end{array}$

Therefore, the odds of all three students have blue eyesis $\frac{11}{184}$ .