EXAMPLE 4.20 College Students

Here is the distribution of U.S. college students classified by age and full-time or part-time status:

Let's compute the probability that a student is aged 15 to 19, given that the student is full-time. We know that the probability that a student is full-time and aged 15 to 19 is 0.21 from the table of probabilities. But what we want here is a conditional probability, given that a student is full-time. Rather than asking about age among all students, we restrict our attention to the subpopulation of students who are full-time. Let

Our formula is

We read from the table as mentioned previously. What about ? This is the probability that a student is full-time. Notice that there are four groups of students in our table that fit this description. To find the probability needed, we add the entries:

200

We are now ready to complete the calculation of the conditional probability:

The probability that a student is 15 to 19 years of age, given that the student is fulltime, is 0.31.