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Just as a pedagogical exercise... you could say that after 4 flips the following are possible: Real coin HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT Fake coin HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH Since we know the first three flips are Heads, we eliminate all cases that don't begin with HHH. Tha leaves us: Real coin: HHHH HHHT Fake coin: HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH HHHH There are 18 possibilities. 17 of them have Heads on the 4th flip. P(H on 4th) = 17/18. Same as what you did, but a little more direct.