EXAMPLE 4.5 Sample Space for Tossing a Coin Four Times

Toss a coin four times and record the results. That's a bit vague. To be exact, record the results of each of the four tosses in order. A possible outcome is then HTTH. Counting shows that there are 16 possible outcomes. The sample space is the set of all 16 strings of four toss results—that is, strings of H's and T's.

Suppose that our only interest is the number of heads in four tosses. Now we can be exact in a simpler fashion. The random phenomenon is to toss a coin four times and count the number of heads. The sample space contains only five outcomes:

This example illustrates the importance of carefully specifying what constitutes an individual outcome.