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Suppose we roll a fair six-sided die and then flip a number of fair coins equal to the number…

 Suppose we roll a fair six-sided die and then flip a number of fair coins equal to the number showing on the die. (For example, if the die shows 4, then we flip 4 coins.) (a) What is the probability that the number of heads equals 3? (b) Conditional on knowing that the number of heads equals 3, what is the conditional probability that the die showed the number 5?