Each year, millions of people travel to casinos hoping they will come away richer. Many more people visit their local supermarket each day to bet with lottery cards. People play the stock market, join in the office football pool, and meet with friends on the weekend for a game of poker. Why do we invest this money on chance? We do it because we believe we can beat the odds. We believe in the possibility of winning.

Mathematical principles can tell us more than whether it is possible to win. They can tell us how often we are likely to win. The mathematical concept that deals with the chances of winning a lottery drawing or a poker game is probability. If we can determine the probability that a certain event (such as winning the lottery) will occur, we can make a better choice about whether to risk the odds.

Determining probability

How do we determine probability? Let's say there are 12 socks in your dresser drawer. Five are red and 7 are blue. If you were to close your eyes, reach into the drawer, and draw out 1 sock, what is the probability that it would be a red sock? Five of the 12 socks are red, so your chances of picking a red sock are 5 out of 12. You can set this up as a fraction or a percentage that expresses the probability of picking a red sock:

5/12

Your chances of picking a red sock are 5 out of 12, or 5 divided by 12, which is about 42%. Not bad, as odds go.

Imagine you're choosing between 2 colleges, 1 in California and 1 in Massachusetts. You decide to flip a coin. Heads, you'll go to California. Tails, you'll go to Massachusetts. When you toss the coin, what is the probability that the head side of the coin will be facing up once the coin hits the floor? There are 2 sides to a coin, and 1 of them is heads, so your odds are 1 out of 2. In other words:

1/2

One divided by 2: that's a 50% chance of heads, and therefore also a 50% chance of tails. The odds are equal. You're as likely to go to California as to Massachusetts if you base your decision on a coin toss.

Even if you don't frequent casinos, you probably play the odds all the time. You might invest in the stock market. You might buy auto, health, and life insurance as a hedge against the costs of damage or injury. In many cases in which you are trying to predict the future, you're using the mathematics of probability.

How do casinos stay in business? Find out more in "Place Your Bets: Cashing in on Probability."