# An interesting math club problem

Here is a problem a student in math club came up with, and we spent the period trying to solve it. It was great because we had to think about it in different ways and use various problem solving strategies. Elation, frustration, desire to give up, being convinced by others, talking myself out of my own thinking… all the things that happen during the working through of good problems happened! I think we solved it, but I’m not totally sure. Regardless, obsessively fun.

Have a crack at it!

You have a school with 200 students in it. Every student is friends with 4 other students (however if A is friends with B, B doesn’t have to be friends with A). (You can assume the friendships are random.) 30 of the 200 students are in a play.

What is the probability that randomly selected student who is not in the play has a friend who is in the play?

The extension: Same scenario and question, but 60 of the 200 kids have 6 friends each, 100 kids have 5 friends each, and 40 kids have 4 friends each.

Look below for the probabilities we got (without any work shown!).

We got around 48% for the first answer and around 58% for the extension. Any confirmation or de-confirmation of these answers would be helpful!