EXAMPLE 1 Marital status of young women

Look again at the probabilities for the marital status of young women. Each of the four probabilities is a number between 0 and 1. Their sum is

0.478 + 0.476 + 0.004 + 0.042 = 1

This assignment of probabilities satisfies Rules A and B. Any assignment of probabilities to all individual outcomes that satisfies Rules A and B is legitimate. That is, it makes sense as a set of probabilities. Rules C and D are then automatically true. Here is an example of the use of Rule C.

The probability that the woman we draw is not married is, by Rule C,

P(not married) = 1 − P(married)

= 1 − 0.476 = 0.524

That is, if 47.6% are married, then the remaining 52.4% are not married. Rule D says that you can also find the probability that a woman is not married by adding the probabilities of the three distinct ways of being not married, as we did earlier. This gives the same result.