Probability. When we say that one event is more probable than another, we mean it is more likely to happen. The branch of mathematics called probability tries to express in numbers statements of the form: An event A is more (or less) probable than an event B.
If a person tosses a coin, there are only two ways it can fall—heads or tails. It is as likely to fall one way as the other. Thus we say that the probability of throwing heads is 1/2. If the coin is tossed 100 times and x is the number of times heads occurs, we can expect the ratio x/100 to be close to 1/2. More generally, if a coin is tossed n times and x is the number of times heads occurs, the ratio x/n will be very close to 1/2 if n is very large.
Now suppose a person tosses three coins. There are eight possible outcomes: hhh, hht, hth, thh, htt, tht, tth, and ttt. Three of these outcomes have two heads, so the probability of throwing two heads is 3/8. Only one outcome has exactly three heads, so the probability of throwing three heads is 1/8. The event two heads is more probable than the event three heads. If a set of three coins is tossed a very large number of times, we would expect two heads to occur very nearly 3/8 of the time and three heads to occur very nearly 1/8 of the time.
Probability is the foundation of the science of statistics. A political scientist, for example, may gather data and use statistics to predict the percentage of voters who will vote for a particular candidate in an election. The political scientist then uses probability to calculate the possible error of the estimate.
See also Fermat, Pierre de; Pascal, Blaise; Statistics.
