Question 1009064: 5. A basketball player has an overall 60% average of success while shooting free
throws.
(a) After a foul, she gets ready to make two free throws. One of your students
says “she’s bound to make at least one of the two, since 2×60% > 100%”.
What is the problem with this argument? Explain.
(b) If each successful free throw is worth one point, what is the expected
number of points she’ll make after the foul?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A basketball player has an overall 60% average of success while shooting free
throws.
(a) After a foul, she gets ready to make two free throws. One of your students
says “she’s bound to make at least one of the two, since 2×60% > 100%”.
What is the problem with this argument? Explain.
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The events (shooting 2 free throws) are independent events.
P(she makes both shots) = 0.6*0.6 = 0.36
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(b) If each successful free throw is worth one point, what is the expected
number of points she’ll make after the foul?
Random point value::..............0........1...........2
Corresponding probabilities::....0.4^2..2*0.6*0.4....0.6^2
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Expected point value:: 0.16*0 + 2*0.24*1 + 0.36*2 = 0.48+0.72 = 1.2
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Cheers,
Stan H.
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