A Fairground Problem … BiBa

You are at a fairground, and there’s a fun challenge. In front of you are five bins, and the challenge is for you to fire a ball at the bins, and where they will fall randomly into one of the bins. If you get two balls in the bin, you will win, but every attempt will cost you $1. The prize money is $4. Is it a good bet?

Okay. You have five bins, and you want to get to the point where one bin has two balls. For this…