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Chapter 2: Problem 69

In a survey of 150 students, 90 were taking mathematics and 30 were taking psychology. a. What is the least number of students who could have been taking both courses? b. What is the greatest number of students who could have been taking both courses? c. What is the greatest number of students who could have been taking neither course?

Short Answer

Expert verified
a. The least number of students who could have been taking both courses is 0.\nb. The greatest number of students who could have been taking both courses is 30.\nc. The greatest number of students who could have been taking neither course is 30.

Step by step solution

01

Determine the possible number of students taking both courses

If we don't have more information about the students, the least number of students who could have been taking both courses is zero. This is the case where all students taking mathematics are not taking psychology and vice versa.
02

Determine the greatest number of students taking both courses

In this case, the greatest number of students who could have been taking both courses is the smaller of the two numbers given, which is 30. This situation happens when all the 30 students taking psychology are the same students among those taking mathematics. Therefore, these 30 students are taking both courses.
03

Determine the greatest number of students taking neither course

For this case, the greatest number of students who could be taking neither course is the result of subtracting the total number of students taking mathematics and psychology (90 + 30 = 120) from the total number of students surveyed, which is 150. In this case, the calculation is 150 - 120 = 30. This situation considers that no student is taking both courses, meaning that all 120 students taking either mathematics or psychology are different individuals. The remaining 30 students are not taking either of the two courses.

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