# 6.2. Basketball

> You have a basketball hoop and someone says that you can play one of two games. Game 1: You get one shot to make the hoop. Game 2: You get three shots and you have to make two of three shots. If p is the probability of making a particular shot, for which values of p should you pick one game or the other?

p of game2 is p(2/3) + p(3/3) = 3(p-1) * p ^ 2 + p ^ 3 = 3p2 - 2p3.

You should play game1 if p > 3p2 - 2p3; (2p - 1)(p - 1) > 0

(see book). 2p - 1 < 0; p < 0.5.

If p < 0.5, play the first game. Else, play game 2. If p=0, p=0.5, p=1, doesn't matter.