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I am having troubles understanding how to tackle the following question. The probability of getting tails when tossing a coin is $p=1/2$. I toss the coin n times, and want to determine the probability of getting r tails in a row ($r<n$).

Im thinking that there are $ ^nC_r$ ways that we can get r tails in a row when tossing the coin n times. The probability to not get a tail is also 1/2, so the probability of getting r tails in a row when tossing n times should be: $P$=$ ^nC_r \cdot (1/2)^r \cdot (1/2)^{(n-r)}$ ?

JMP
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Simply Wondering
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  • Suppose you get the sequence $\color{red}{tt}h \color{red}{tt}h \color{red}{ ttt}$. How many two tails in a row you count? – callculus42 Jan 25 '23 at 20:06
  • 3... but how would i describe it mathematically? – Simply Wondering Jan 25 '23 at 20:13
  • I don't hav a full solution yet. But you can start with $x=ttt$. Then a sequence with a length of $n=8$ has the forms $xhxh, hxhx, xhhx,$ $hhhhhx, hhhhxh, .. $. This is how you can start. – callculus42 Jan 25 '23 at 20:29
  • See also https://math.stackexchange.com/questions/59738/probability-for-the-length-of-the-longest-run-in-n-bernoulli-trials/59749#59749 for an exact answer to this question – Mike Earnest Jan 25 '23 at 20:43

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