SOLUTION: Aaron and Jonathan take turns shooting a free throw, with Aaron going first. Whoever makes the first shot wins. The game continues until
someone makes the shot. Aaron has a 40% ch
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-> SOLUTION: Aaron and Jonathan take turns shooting a free throw, with Aaron going first. Whoever makes the first shot wins. The game continues until
someone makes the shot. Aaron has a 40% ch
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Question 1145662: Aaron and Jonathan take turns shooting a free throw, with Aaron going first. Whoever makes the first shot wins. The game continues until
someone makes the shot. Aaron has a 40% chance of making a free throw, while Jonathan has a 50% chance. What is Aaron’s chance of
winning the game? Answer by greenestamps(13200) (Show Source):
P(Aaron wins on his second shot) = (3/5)*(1/2)*(2/5) = 3/25
(Aaron misses on his first, probability 3/5; then Jonathan misses on his first, probability 1/2; then Aaron makes his second shot probability 2/5)
P(Aaron wins on his third shot) = (3/5)*(1/2)*(3/5)*(1/2)*(2/5) = 9/250
etc., etc., etc.....
The sum of the probabilities is a geometric progression with first term 2/5 and common ratio (3/5)*(1/2) = 3/10.
The probability that Aaron wins is the sum of that infinite geometric progression:
