Chapter 6.8, Problem 28E

To determine

To calculate the odds in favor and odds against.

Answer to Problem 28E

The odds in favor is $\frac{3}{4}$ or $\text{3 to 4}$ .

The odd against is $\frac{4}{3}$ or $\text{4 to 3}$ .

Explanation of Solution

Given information:

Number of $\text{\$1}$ bills is $4$ .

Number of $\$5$ bills is $2$ .

Number of $\$20$ bills is $1$ .

Formula used:

  $\begin{array}{l}\text{Odds in favor}=\frac{\text{Number of favorable outcomes}}{\text{Number of unfavorable outcomes}}\\ \text{Odds against}=\frac{\text{Number of unfavorable outcomes}}{\text{Number of favorable outcomes}}\end{array}$

Calculation :

Total number of outcome $=4+2+1=7$ .

Number of favorable outcomes of choosing a bill greater than $\$1=2+1=3$ .

Number of unfavorable outcomes of choosing a bill greater than $\$1=7-3=4$ .

Therefore,

  $\begin{array}{l}\text{Odds in favor}=\frac{\text{Number of favorable outcomes}}{\text{Number of unfavorable outcomes}}=\frac{3}{4}\\ \text{Odds against}=\frac{\text{Number of unfavorable outcomes}}{\text{Number of favorable outcomes}}=\frac{4}{3}\end{array}$

Hence,

The odds in favor is $\frac{3}{4}$ , or $\text{3 to 4}$ , that a bill is chosen greater than $\text{\$1}$ .

The odds against is $\frac{4}{3}$ , or $\text{4 to 3}$ , that a bill is chosen greater than $\text{\$1}$ .