Thread: Friends Proof

Hey there I need some help with this math problem.

In a class with 24 students the students are polled and asked how many members of the class they are friends with. The result of the poll is as follows: Three said they are friends with 4 people in the class; four said they are friends with 5 people in the class; six said they are friends with 7 people in the class; seven said they are friends with 9 people in the class; and four said they are friends with 11 people in the class Explain why some student most have miscounted their number of friends.

I understand how this works conceptually, but am hoping someone can guide and explain each step to me on how to go about solving this problem as a proof thanks.

Hey gfbrd.

This will involve showing intersection terms along the lines of where P(A OR B) = P(A) + P(B) - P(A and B) and if you have intersection terms then you will have the phenomenon of over-counting.

So can you show if an interaction term of P(A and B) occurs where A and B are the different events where the term is non-zero?

um.. sorry lol i kinda forgotten what i learned from statistics so just correct me if im wrong, this is all i can get for now
so for the 3 people that said they know 4 friends each that would mean the probability of each one of the 3 is 4/24 = 1/6
for the 4 people that said they know 5 friends each the probability of each one of the 4 is 5/24
for the 6 people that said they know 7 friends each the probability of each one of the 7/24
for the 7 people that said they know 9 friends each the probability of each one of the 9/24 = 3/8
for the 4 people that said they know 11 friends each the probability of each one of the = 11/24

The idea is just to look for overlap in the events and the best way I could think of was to use probability statements like P(A and B).

You have listed that you have 5 events with {4,5,7,9,11} friends for each event so if one event is A and another is B then P(A and B) != 0 for A != B in order to count something twice between two events. If you can find where this happens then you can calculate the intersection and show how much over-counting has occured.

If you show your conceptual proof, I'll try and relate this to the formal statements.

Well the conceptual idea I have is that if a student A has 4 friends, it could be any 4 in the class and lets say he is friends with student B, so the friend count is 1, but at the same time student B will count his number of friends as well, so student B will count student A as his friends, if everyone does this theres going to be a over counting in friends.

Not sure how I can make a proof from that though.