EXAMPLE 1 Coin tossing

When you toss a coin, there are only two possible outcomes, heads or tails. Figure 17.1 shows the results of tossing a coin 1000 times. For each number of tosses from 1 to 1000, we have plotted the proportion of those tosses that gave a head. The first toss was a head, so the proportion of heads starts at 1. The second toss was a tail, reducing the proportion of heads to 0.5 after two tosses. The next four tosses were tails followed by a head, so the proportion of heads after seven tosses is 27, or 0.286.

The proportion of tosses that produce heads is quite variable at first, but it settles down as we make more and more tosses. Eventually, this proportion gets close to 0.5 and stays there. We say that 0.5 is the probability of a head. The probability 0.5 appears as a horizontal line on the graph.