EXAMPLE 4 Classical method: Single fair die

Recall the town fair example (page 240). In the game, you win if you roll a 6 on a single roll of a single fair die. Find the probability of winning the game.

Solution

The sample space for a single die toss consists of six outcomes, . When the six outcomes are equally likely, we say that the die is fair. If the outcomes are not equally likely, then the die is loaded or defective. If we assume the die is fair, then, because the sum of the probabilities of the outcomes must equal 1, the probability of any particular outcome must equal , using the classical method. We write