sequence of HHH before THH

Asked Aug 11 '24 at 09:59

Active Aug 11 '24 at 09:59

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Question: You keep flipping a coin until you get either HHH or THH. What is the probability that you get a HHH sequence before THH?

What is wrong with my reasoning here: You have an equal probability of getting T or H on the first flip. After that for both sequences, you just need to get HH so they have equal probability. That means the probability of getting HHH before THH is $\frac{1}{2}$.

asked Aug 11 '24 at 09:59

Apex345

the only way of getting HHH before THH is to get H on the first 3 flips; if you feel uncertain, think about three case when the 1st 3 flips give HHT – user8268 Aug 11 '24 at 10:07
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$HHH$ wins only if the start is $HHH$ , as soon as $T$ appears , $THH$ will win. – Peter Aug 11 '24 at 10:07
This is discussed in Pennies game (hope the spelling is correct). The paradox is that for every sequence there is a countersequence beating it in the sense that the chance it comes first is higher. – Peter Aug 11 '24 at 10:08
See Penney's Game – lulu Aug 11 '24 at 10:16
Thank you lulu , so I actually did not correctly remember it ... – Peter Aug 11 '24 at 10:22

sequence of HHH before THH

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