Q. If tossing a fair coin, how many tosses does it take to get two heads in a row, on average?

Question

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I was a bit unsure about what 'on average' meant. I'm a bit unsure about what I tried:

I considered cases of getting two heads in a row for increasing total tosses and considered each of their probabilities as such to take an average:

HH - 0.25
THH - 0.125
TTHH - 1/16
And so on, until 8 tosses

But it wouldn't make sense because it would end up being an infinite series.

Also, I've found that the answer is 6, but I'm more interested in how to get there. Thanks.

Answer 1

google is you friend. You might start here:

https://www.quora.com/What-is-the-expected-number-of-coin-flips-until-you-get-two-heads-in-a-row

Answer 2

Thanks! This clears it up.