Questions: 18. For a survey of 110 law school students, it was found that: 50 took Probate Law, 70 took Criminal Law, and 24 took Criminal Law but not Probate Law. How many of the students took exactly one of these courses?

Solution Steps

To find the number of students who took exactly one of the courses, we need to determine the number of students who took only Probate Law and the number of students who took only Criminal Law. We can use the principle of inclusion-exclusion to find the number of students who took both courses and then subtract appropriately.

1. Calculate the number of students who took both Probate Law and Criminal Law.
2. Calculate the number of students who took only Probate Law.
3. Calculate the number of students who took only Criminal Law.
4. Sum the students who took only Probate Law and only Criminal Law to get the total number of students who took exactly one course.

Given:

• Total students: \(110\)
• Students who took Probate Law: \(50\)
• Students who took Criminal Law: \(70\)
• Students who took Criminal Law but not Probate Law: \(24\)

We need to find the number of students who took both Probate Law and Criminal Law. This can be calculated as: \[ \text{both\_courses} = \text{criminal\_law} - \text{criminal\_not\_probate} = 70 - 24 = 46 \]

The number of students who took only Probate Law can be calculated by subtracting the number of students who took both courses from the total number of students who took Probate Law: \[ \text{only\_probate} = \text{probate\_law} - \text{both\_courses} = 50 - 46 = 4 \]

The number of students who took only Criminal Law is given directly as: \[ \text{only\_criminal} = \text{criminal\_not\_probate} = 24 \]

The total number of students who took exactly one course is the sum of the students who took only Probate Law and the students who took only Criminal Law: \[ \text{exactly\_one\_course} = \text{only\_probate} + \text{only\_criminal} = 4 + 24 = 28 \]

Final Answer