
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.

Re: Friends Proof
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 overcounting.
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 nonzero?

Re: Friends Proof
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

Re: Friends Proof
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 overcounting has occured.
If you show your conceptual proof, I'll try and relate this to the formal statements.

Re: Friends Proof
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.