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A coin lands heads with probability p. For which p is it most likely that the pattern HT is first completed exactly on the fifth toss?

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A coin lands heads with probability 1/4. What is the expected number of flips needed to see three heads?A stock is at $100 and each day a coin flip moves it up $1 on Heads or down $1 on Tails. What is the probability it is exactly $100 after 10 days?A fair coin is tossed repeatedly. A wins if HTH appears first, B wins if HTT appears first. What is the probability that A wins?

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