Chapter 13.3, Problem 31E

To determine

To find: The odds of 2 brown and 1 blue eyes.

Answer to Problem 31E

The odds of 2 brown and 1 blue eyesis $\frac{22}{53}$ .

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 2 brown and 1 blue eyes calculated as,

  $\begin{array}{c}P\left(\text{s}\right)=\frac{C\left(13,2\right)\cdot C\left(11,1\right)}{C\left(27,3\right)}\\ =\frac{858}{2925}\\ =\frac{22}{75}\end{array}$

The probability of failure is calculated as,

  $\begin{array}{c}P\left(f\right)=1-P\left(s\right)\\ =1-\frac{22}{75}\\ =\frac{53}{75}\end{array}$

The odds of 2 brown and 1 blue eyesis calculated as,

  $\begin{array}{c}\text{Odds}=\frac{P\left(s\right)}{P\left(f\right)}\\ =\frac{22/75}{53/75}\\ =\frac{22}{53}\end{array}$

Therefore, the odds of 2 brown and 1 blue eyesis $\frac{22}{53}$ .