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I am wondering how to do this problem. I have a way that gave me the correct answer but I would not want to do this every time or for large numbers.

What I did:

So 2^5 equals 32 since the probability is 1/2 and I want 5 flips. Then I have 4 ways that the 2nd head will land on the 5th flip. So I have 4/32. which is 12.5%

I also tried Binomial distribution but did not get the correct answer.

5C2(.5)^2(.5)^3. I know that this will not work since the second head can be in any location but do not remember how I can make it work for this problem or if it would even work.