Final answer:
There were 149 individuals aged 18-24 who only hung out with friends last Friday night.
Step-by-step explanation:
Let's denote the sets as follows:
- A : Those who watched TV
- B : Those who ate pizza
- C : Those who hung out with friends
We are given the following information:
|A| = 186
|B| = 185
|A ∩ B ∩ C'| = 38
|A ∩ C ∩ B'| = 36
|B ∩ C ∩ A'| = 35
|A ∩ B ∩ C| = 37
|U| = 545 (where U is the universal set)
And we know that |A' ∩ B' ∩ C'| = 77 (those who did not do any of these activities).
We can use the principle of inclusion-exclusion to find the number of people who only hung out with friends:
|A ∩ B' ∩ C| = |A| - |A ∩ B ∩ C'| - |A ∩ C ∩ B'| + |A ∩ B ∩ C|
Substitute the given values:
|A ∩ B' ∩ C| = 186 - 38 - 36 + 37
|A ∩ B' ∩ C| = 149
So, there were 149 individuals who only hung out with friends last Friday night.
Your complete question is: A survey of 545 adults aged 18-24 year olds was conducted in which they were asked what they did last Friday night. It found: - 186 watched TV - 185 ate pizza - 38 watched TV and ate pizza, but did not hang out with friends - 36 watched TV and hung out with friends, but did not eat pizza - 35 hung out with friends and ate pizza, but did not watch TV - 37 watched TV, hung out with friends, and ate pizza - 77 did not do any of these three activities How may 18-24 year olds (of these three activities) only hung out with friends last Friday night?