INTERPRETING ODDS

Often probabilities are stated in the media in terms of odds. For example, the following is a paragraph from Roxy Roxborough's Odds and Ends column in USA Today .

``` EYE OF THE TIGER: Sensational PGA tour rookie Tiger Woods has been installed an early 9-5 favorite to win the most cash at the Skins Game at the Rancho La Quinta Golf Course in La Quinta, Calif., Nov. 30-Dec. 1. The charismatic Woods will have to contend with Fred Couples, the close 2-1 second choice, as well as the still dangerous Tom Watson, 3-1, and power stroker John Daly, 9-2. ```

We read that Tiger Woods is the favorite to win this golf tournament at a 9-5 odds. What does this mean?

An odds of an event is the ratio of the probability that the event will not occur to the probability that the event will occur . In our example, the event is "Tiger Woods will win". We read that the odds of this event are 9 to 5 or 9/5. This means that

` `

``````   Probability (Tiger Woods will not win)      9
--------------------------------------  =  ---
Probability (Tiger Wodds will win)        5
``````
` `

This means that it is more likely for Woods to lose the tournament than win the tournament.

How can we convert odds to probabilities? There is a simple recipe. If the odds of an event are stated as A to B (or A-B or A/B), then the probability of the event is

` `

``````                           B
Probability(event) = ----------
B + A
``````
` `

So, for example, if the odds of Woods winning are 9-5 or 9/5, then the probability of Woods winning is

` `

``````                           5
Probability(event) = ---------- = .3571
5 + 9
``````
` `

QUESTIONS:

From the article above, find the probabilities that Couples, Watson, and Daly each win the golf tournament. What is the probability that a long-hitter (Woods or Daly) will win the tournament? What is the probability that Watson will not win the tournament?

Page Author: Jim Albert (© 1996)
albert@bayes.bgsu.edu
Document: http://www-math.bgsu.edu/~albert/m115/probability/odds.html