SOLUTION: A basketball player makes 70% of her throws when she is in a two-shot free throw situation (she gets two shots no matter what). Her coach notices that she gets nervous in a one-an

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Question 1181930: A basketball player makes 70% of her throws when she is in a two-shot free throw situation (she gets two shots no
matter what). Her coach notices that she gets nervous in a one-and-one free throw situation (here she only gets to take
a second shot if she makes the first) and makes 50% of those free throws.
A) Construct an area model for each of the player’s free throw situations, mapping the chance of getting 0, 1, or 2
points).
B) What is the player’s average points per attempt for each of the two scenarios? Two shot vs. One-and-one.
C) Suppose the player was fouled 50 times this season. Of these, 20 were two-shot free throw situations and 30 were
one-and-one free throw situations. How many points would you expect her to have scored for free throws this season?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
A) Let X = r.v. equal to shots made from a free throw situation. The possible values of X are 0, 1, or 2.
Two-shot: P%28X=0%29+=+C%282%2C0%29%2A0.7%5E0%2A0.3%5E2+=+0.09
P%28X=1%29+=+C%282%2C1%29%2A0.7%5E1%2A0.3%5E1+=+0.42, and P%28X=2%29+=+C%282%2C2%29%2A0.7%5E2%2A0.3%5E0+=+0.49
1-and-1: P%28X=0%29+=+0.50, P%28X=1%29+=+0.50%2A0.50++=0.25, and P%28X=2%29+=+0.50%2A0.50++=0.25.

B) 2-shot: E%28X%29+=+0%2A0.09+%2B+1%2A0.42+%2B+2%2A0.49+=+1.4
1-and-1: E%28X%29+=+0%2A0.50+%2B+1%2A0.25+%2B+2%2A0.25+=+0.75

C) 2-shot: 20*1.4 = 28
1-and-1: 30*0.75 = 22.5
She would be expected to score highlight%2850.5%29 points from free throws that season.