Statistics: Conditional Probability

Sometimes you have more information than simply total outcomes and favorable outcomes and, hence, are able to make more informed judgments regarding probabilities. For example, suppose you know the following information: In a particular village, there are 60 women and 40 men. Twenty of those women are 70 years of age or older; 5 of the men are 70 years of age or older. See Table 1 .

TABLE 1

Distribution of People in a Particular Village

	*70+ years*	*69 or less*	*Totals*
Women	20	40	60
Men	5	35	40
Totals	25	75	100

What is the probability that a person selected at random in that town will be a woman? Because women constitute 60 percent of the total population, the probability is .60.

What is the probability that a person 70+ years of age selected at random will be a woman? This question is different because the probability of A (being a woman) given B (the person in question is 70+ years of age) is now conditional upon B (being 70+ years of age). Because women number 20 out of the 25 people in the 70+ years-old group, the probability of this latter question is 20/25, or .80.

Conditional probability is found using this formula: