Chapter 6.7, Problem 20E

To determine

To find : the probability of an event with even odds.

Answer to Problem 20E

If the probability of the event is $P\left(A\right)$ then odd in favour is $\frac{P\left(A\right)}{1-P\left(A\right)}$ and odd against is $\frac{1-P\left(A\right)}{P\left(A\right)}$ .

Explanation of Solution

Given information :

An event has even odds when the odds in favour of (or against) the event are 1:1.

Calculation :

The even odds when the odds in favour is 1:1.

So,

  $\begin{array}{l}\text{Odd in favor}=\frac{\text{Number of favourable outcome}}{\text{Number of unfavourable outcome}}\\ \text{Odd in favor}=\frac{\text{1}}{\text{1}}\end{array}$

Therefore, the probability of the event with even odds

  $\begin{array}{l}P\left(\text{Even odds}\right)=\frac{\text{Number of favourable outcome}}{\text{Number of favourable outcome}+\text{Number of unfavourable outcome}}\\ P\left(\text{Even odds}\right)=\frac{\text{1}}{\text{1}+\text{1}}\\ P\left(\text{Even odds}\right)=\frac{\text{1}}{2}\end{array}$

Hence,

The probability of an event with odds is $\frac{\text{1}}{2}$ .