Chapter 12.7, Problem 38PPE

To determine

To find: The probability of event A.

Answer to Problem 38PPE

The probability of event A is $\frac{1}{2}$ .

Explanation of Solution

Given:

It is given that the odds in favor of event A are equal to the odds against event A.

Calculation:

The odds in favor of an event is given by, $\text{odds in favor of an event}=\frac{\text{number}\text{of}\text{favorable}\text{outcomes}}{\text{number}\text{of}\text{unfavorable}\text{outcomes}}$ .

The against an event is given by $\text{odds against an event}=\frac{\text{number}\text{of}\text{unfavorable}\text{outcomes}}{\text{number}\text{of}\text{favorable}\text{outcomes}}$ .

These two odds will be equation if numbers of favorable outcomes are equal to the number of unfavorable outcomes.

So, number of favorable outcomes, and number of unfavorable outcomes will be 1.

The probability of an event A will be as follows.

  $\begin{array}{c}P=\frac{1}{1+1}\\ =\frac{1}{2}\end{array}$

Therefore, the probability of event A is $\frac{1}{2}$ .