# Need help with probability closed form expression

Probability that a sequence of x coin flips will contain TH. How exactly would I approach this problem? Just need hints to direct me in the right direction.

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If the sequence doesn't contain $TH$, then each $T$ is followed by another $T$. So a $TH$-free sequence is just a (possibly empty) run of $H$'s followed by a (possibly empty) run of $T$'s. How many of these are there? –  mjqxxxx Feb 6 '13 at 23:37
Is it (.5^n+.5^n) ? –  John Feb 6 '13 at 23:43
@Koy No, think through what mjpxxx said. It might help to list out the cases for say $n=5$. –  Calvin Lin Feb 6 '13 at 23:46
(.5^n)(1-.5)^n? I'm just guessing in the dark now. –  John Feb 6 '13 at 23:52
Don't guess, do what @Calvin suggested. Write 'em out for $n=5$. –  Gerry Myerson Feb 7 '13 at 2:23