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Basket Ball Puzzle : One or 2 of 3

October 29, 2009, 8:36 pm

You have a basket ball hoop and someone says that you can play 1 of 2 games. You get $1000 and one shot to get the hoop. Or, you get three shots and you have to make 2 of 3 shots. Which one do you choose? If p is the probability of making a particular shot, what value of p makes you switch games?

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One Comment

  1. syam says:
    October 29, 2009 at 8:39 pm
    Expected value of one shot game, E1 = 1000p
Expected value of three shot game, E3 = 1000(probabiliy of making 2 or 3 balls)
= 1000(p^3 + 3p^2(1-p))
= 1000(-2p^3 + 3p2)
Looking at these two expected values, E1 = E3 when when p=1,0, and E3 > E1 when p > 1/2.
In English, it doesn't matter which game I play if p=1 or 0.
If p < 1/2, I'll take game 1. If p > 1/2, I'll take game 2.

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