Recreational Math

Mathematical Games

What is the difference between probability and odds?

Probability is usually expressed as a fraction (sometimes as a percentage). For example, if there are ten pieces of fruit in a jar—three apples and seven oranges—then the probability of taking out an orange is 7/10 (or seven chances of an orange out of a total of ten chances).

On the other hand, odds are expressed as the number of chances for (or against) versus the number of chances against (or for). Thus, if there are three chances of picking an apple and seven chances of picking an orange, the odds are 7 to 3 against you picking an apple. Just reverse this to find the odds in favor; or, in this example, the odds would be 3 to 7 in favor of picking an apple.

In order to convert the odds to probability, just add the chances. Thus, if the odds against a horse winning the Kentucky Derby are 4 to 1, that means that, out of 5 (or 4 + 1) chances, the horse has one chance of winning. That makes the probability of the horse winning 1/5, or 20 percent.


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