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 pick-

ing 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.

What are the oddsof winning the powerball lottery?

It was eventually going to happen: A number of lottery-offering states got together to

have lotteries with huge amounts of prize money. The resulting powerball lotteries

have been very lucrative—not for the players, but for the states. Such gigantic sums of

money tempt quite a few people to take the risk, with many buying hundreds of tickets

in an attempt to better their odds.

But does it work? Not really. There is a way to determine the odds of such “lotto-

type” lotteries in which numbered balls (or numbers) are randomly chosen to repre-

sent a winning number. This is usually expressed as: n! / (n r)! r!, in which n is the

highest numbered ball and r is the number of balls chosen. (The n! is “n-factorial”; for

more information about factorials, see “Algebra.”)

In math, this type of equation is called a combination. For example, if there are 50

balls and 5 are chosen, there are 50 possible numbers that can come up first, leaving

49 that can come up second, and so on. The equation becomes:

or the chances of winning are about 2 million to 1.

But don’t think that powerball lotteries give a person an edge. For example, a

powerball lottery can be one in which 5 out of 50 balls (or numbers) are drawn, with

an extra powerball pulled out of a different number of balls. This is notlike figuring

the odds for a “drawing 6 out of 50 balls” contest, but is actually two separate lotteries:

one with 5 out of 50 balls and one with the powerball group.

The probability of matching the first 5 balls is determined as above. But the

powerball is separate: For instance, say the powerball is taken from a group of 36,

making the powerball group’s odds 36:1. The probability of winning the entire jackpot

can be determined by adding this to the results of the 5-ball draw. Now the odds

become even higher: The 50/5 drawing a powerball of 36 (2,118,760 36):1 

76,275,360:1 or about 76 million to one. There are even worse odds if more balls are in

the powerball group.

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