Eli5: If I flip a coin 10x what’s the chances that the next 10 flips will be the exact outcome of the first 10?
In: Mathematics
If you just mean the sum of heads in the first 10 vs the sum of heads in the second 10, then you’d calculate the likelihood for each number (0 heads, 1 head, 2 heads, … 10 heads), then square them for the odds of getting the same result twice in a row. Add those squared numbers and you’d get the overall odds, which comes out to 17.6197052%
For instance…
0 heads. The odds of that happening are 1 in 1024. So in those 1 out of 1024 times, you have 1 out of 1024 odds of it happening again, so roughly 1 in a million.
5 heads — the odds of getting 5 heads is 252 in 1024 (~24.6%). The odds of getting 5 heads AGAIN is 252 out of 1024, so the odds of that happening are 252^2 / 1024^2, or around 6%.
Just to verify, I wrote a quick and dirty program to actually do this 100 million times… It happened to get 17.617303%
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