EXAMPLE 4.6

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 typical outcome is then HTTH. Counting shows that there are 16 possible outcomes. The sample space S is the set of all 16 strings of four 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:

S = {0, 1, 2, 3, 4}

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