Chapter 13.3, Problem 12CFU

To determine

To find: The odds that it will not rain on Saturday.

Answer to Problem 12CFU

The odds that it will not rain of Saturdayis $\frac{1}{4}$ .

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 getting rain on Saturday is calculated as,

  $\begin{array}{c}P\left(\text{s}\right)=\frac{80}{100}\\ =\frac{4}{5}\end{array}$

The probability of failure is calculated as,

  $\begin{array}{c}P\left(f\right)=1-P\left(s\right)\\ =1-\frac{4}{5}\\ =\frac{1}{5}\end{array}$

The odds of it will not rain on Saturday is calculated as,

  $\begin{array}{c}\text{Odds}=\frac{P\left(f\right)}{P\left(s\right)}\\ =\frac{1/5}{4/5}\\ =\frac{1}{4}\end{array}$

Therefore, the odds that it will not rain of Saturday is $\frac{1}{4}$ .