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Question: rosencrantz and guildenstern are flipping coins guildenstern has a bag...

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Rosencrantz and Guildenstern are flipping coins. Guildenstern has a bag with 100 coins in it. All of them are fair coins, except for 10 that each have heads on both sides and 2 that each have tails on both sides. Guildenstern reaches into the bag without looking, removes a randomly chosen coin, with each of the 100 coins equally likely, and flips it. Give exact answers expressed as simplified fractions.

(a) What is the probability that it is one of the 2-headed coins, given that the flip came up heads?

(b) What is the probability that it is one of the fair coins, given that the flip came up heads?

(c) What is the probability that it is one of the fair coins, given that the flip came up tails?

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