A college survey was taken to determine where students study. Of 107 students surveyed, 65 studied in the cafeteria, 55 studied in the student lounge, 24 studied in both the cafeteria and the student lounge.
To solve this problem, we can use the principle of inclusion-exclusion.
Let's define the following variables:
- A: number of students studying in the cafeteria
- B: number of students studying in the student lounge
We are given that A = 65, B = 55, and the number of students studying in both the cafeteria and the student lounge (intersection of A and B) is 24.
Using the principle of inclusion-exclusion, the total number of students studying in either the cafeteria or the student lounge is given by:
|A ∪ B| = |A| + |B| - |A ∩ B|
Plugging in the given values, we have:
|A ∪ B| = 65 + 55 - 24
Simplifying the expression, we get:
|A ∪ B| = 96
Therefore, a total of 96 students studied in either the cafeteria or the student lounge.