EXAMPLE 17 Addition Rule for mutually exclusive events

The National Center for Education Statistics conducted a survey regarding the living arrangements of 19,735 college students. The results are shown in Table 8.

Table 5.35: Table 8 Contingency table of college student living arrangements
On campus Off campus With parents Total
Females 1,368 5,741 4,103 11,212
Males 1,240 4,170 3,113 8,523
Total 2,608 9,911 7,216 19,735

265

Calculate the following probabilities for a randomly chosen college student:

  1. Lives on campus, .
  2. Lives with parents, .
  3. Lives on campus or with parents, .

Solution

  1. A total of 2,608 of the 19,735 students live on campus, so .
  2. Of the 19,735 students, 7,216 live with parents, so .
  3. Living on campus and living with parents are mutually exclusive. So, by the Addition Rule for Mutually Exclusive Events, .

NOW YOU CAN DO

Exercises 45–48.