Question

A baseball player, Mickey, who bats 310 (or .310) gets an average of 3.1 hits in...

A baseball player, Mickey, who bats 310 (or .310) gets an average of 3.1 hits in ten at bats. We will assume that each time Mickey bats he has a 0.31 probability of getting a hit. This means Mickeys at bats are independent from one another. If we also assume Mickey bats 5 times during a game and that x= the number of hits that Mickey gets then the following probability mass function, p(x), and cumulative distribution function F(x) are reasonable:

x 0 1 2 3 4 5
p(x)      .156 .351 .316 a .032 .003
F(x)      .156 .507 .823 b .997 1.00

g. Assume Mickey bats exactly 5 times (a 5-at-bat-game) in each of four consecutive games. What is the probability he gets 2 hits in exactly 2 of those 4 games? (Getting exactly 2 hits will be called a 2-hit-game.)  

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