Surveys & Cardinal Numbers

1. Surveys & Cardinal Numbers Chapter 2 Section 5

2. Example Out of 40 students, 14 are taking English and 29 are taking chemistry. If 5 students are in both classes, how many students are in neither class? 2 CHEMISTRY ENGLISH 9 5 24 2 ALL STUDENTS

3. Example A survey of 70 students revealed that 35 like folk music, 15 like classical music, and 5 like both. How many students like either folk or classical? 45 CLASSICAL FOLK FORMULA FOR THE CARDINAL NUMBER OF THE UNION OF TWO SETS N(AB) = n(A) + n(B) – n(AB) 30 5 10 25 ALL STUDENTS

4. Example 35 total students. 22 male. 19 business majors. 27 freshmen. 14 male business majors. 17 male freshmen. 15 freshmen business majors. 11 male freshmen business majors. MALE BUSINESS 3 2 1 11 ALL STUDENTS 4 6 2 6 FRESHMEN

5. 2 Example 5 • How many upper-class women non-business majors are in the class? • How many women business majors are in the class? MALE BUSINESS 3 2 1 11 ALL STUDENTS 4 6 2 6 FRESHMEN

6. 50 How many in the experiment? Example 22 tall. 25 green peas. 39 smooth peas. 9 tall and green peas. 17 tall and smooth peas. 20 green and smooth peas. 6 have all. 4 none. TALL GREEN 3 2 2 6 ALL STUDENTS 14 11 4 8 SMOOTH