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At noon, Guildenstern rolls a fair die. If it shows 1 or 2 spots, he eats an apple. If the die shows 3,4,5, or 6 spots, Guildenstern then flips a...
At noon, Guildenstern rolls a fair die. If it shows 1 or 2 spots, he eats an apple. If the die shows 3,4,5, or 6 spots, Guildenstern then flips a fair coin. If the coin shows heads he eats an apple, otherwise he eats a banana.
(a) What is the conditional probability that Guildenstern eats an apple given that the die showed 3 spots?
(b) What is the probability that Guildenstern eats an apple? What is the probability that he eats a banana?
(c) What is the conditional probability that the die showed 3 spots given that Guildenstern eats an apple?
