Chapter 6, Problem 5CR

To determine

To find the difference between the probability that an event occurs and odd in favor of that event.

Answer to Problem 5CR

The probability that an event will occur is the fraction of times you expect to see that event in many trials. Whereas the odds are defined as the probability that the event will occur divided by the probability that the event will not occur.

Explanation of Solution

Given information:

Find the difference between the probability that an event occurs and odd in favor of that event.

The probability that an event will occur is the fraction of times you expect to see that event in many trials. Whereas the odds are defined as the probability that the event will occur divided by the probability that the event will not occur.

If the probability of an event occurring is $Y$ , then the probability of the event not occurring is $1-Y$ .

Example: If the probability of an event is 0.80 (80%), then the probability that the event will not occur is $1-0.80$ = 0.20, or 20%.

The odds of an event represent the ratio of the (probability that the event will occur) / (probability that the event will not occur). This could be expressed as follows:

Odds of event = $\frac{Y}{1-Y}$

So, in this example, if the probability of the event occurring = 0.80, then the odds are

  $\frac{0.80}{1-0.80}$

  $=$$\frac{0.80}{0.20}$

  $=$ 4 (i.e., 4 to 1).