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In: Statistics and Probability

Alex challenged David to a free-throw duel. Alex and David would take turns shooting free throws...

Alex challenged David to a free-throw duel. Alex and David would take turns shooting free throws until someone makes a shot. David makes free throws with probability 0.9. Alex makes free throws with probability 0.45. Assume independence. Round all your answers to 4 decimal places.

a. If David shoots first, what is the probability that Alex is the first one to make a free throw?

b. Alex likes to complain. He says that he should shoot first since his success rate is lower. If Alex shoots first, what is the probability that Alex is the first one to make a free throw?

c. Alex does like to complain. He says that he should have two attempts for each one of David's attempts since his success rate is half of David's. What is the probability that Alex is the first one to make a free throw with these rules? That is, the pattern of attempts is AADAADAAD… instead of ADADAD… in part (b).

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orchestra answered 2 years ago
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