12 lines
580 B
Markdown
12 lines
580 B
Markdown
# 6.2. Basketball
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> 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?
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p of game2 is p(2/3) + p(3/3) = 3(p-1) * p ^ 2 + p ^ 3 = 3p2 - 2p3.
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You should play game1 if p > 3p2 - 2p3; (2p - 1)(p - 1) > 0
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(see book). 2p - 1 < 0; p < 0.5.
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If p < 0.5, play the first game. Else, play game 2. If p=0, p=0.5, p=1, doesn't matter.
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