EXAMPLE 6 Classical method: Tossing a fair coin twice

Find the probability of obtaining one heads and one tails when a fair coin is tossed twice.

Solution

It is reasonable to assume that the outcomes in the sample space {HH, HT, TH, TT} are equally likely. The coin doesn’t remember what occurred at Stage 1, so the probabilities at Stage 2 are precisely the same as at Stage 1. Also, recall from the Law of Total Probability that the sum of the probabilities of all the outcomes in the sample space must equal 1. Thus, each of the four outcomes must have probability . Let be the event that one heads and one tails is obtained. Then , so . Thus,