You are the manager of an NBA team that is going to the playoffs, and you want t

Question

You are the manager of an NBA team that is going to the playoffs, and you want trade for a good free throw shooter in the event that a playoff game comes down to foul shots. You are considering two players, Chris and Darren. Chris is an 80% free throw shooter for the first shot. If he makes his first shot he makes the second shot 90% of the time, and if he misses the first shot he makes the second shot 75% of the time. Darren is an 83% free throw shooter for the first shot. If he makes his first shot he makes the second shot 87% of the time, and if he misses his first shot he makes his second shot 80% of the time. Who would you pick? Explain.

Explanation / Answer

let A=event of making shot in first chance

B=event of making shot in second chanre

A'=event of not making shot in first chance

here there are two times to make shot and we find the expected value of making shot in two chance in the following way

P(A)+P(A)*P(B|A)+P(A')*P(B|A')

for chirs P(A)=0.8, P(A')=1-P(A)=1-0.8=0.2, P(B|A)=0.9 and P(B|A')=0.75

the expected value of chirs to make shot=0.8+0.8*0.9+0.2*0.75=1.67

similarly the expected value of Darren to make shot=0.83+0.83*0.87+0.17*0.8=1.6881

since the expected value of Darren is more so picking of Darren should be traded

answer is Darren should be picked.

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