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Find the expected value for the number of flips you'll need to make in order to see the pattern TXT, where T is tails, and X is either heads or tails.

I tried conditioning on the coin flips (e.g. TXT, TXH, H) but I got an incorrect answer of 8. Any suggestions?

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Try to find the expected value for the number of flips until TT and then add 1 because X can just be ignored otherwise.

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