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Consider 9 flips of a fair coin. Let X be the random variable that is the total number of tails. Note that X can be

Consider 9 flips of a fair coin. Let X be the random variable that is the total number of tails. Note that X can be any nonnegative integer from 0 to 9. Let Y be the random variable that is the number of heads in the last flip (can be 0 or 1). What is the probability that simultaneously X=1 and Y=1? (Hint: List all 9 bit strings that have a H in the last flip, and a single T overall.)

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