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
Probability questions often come down to precise wording of exactly what you mean.
If the ordering matters, you need each of your 10 new flips to hit a particular option (so if the first of your first 10 flips was a head, you need the first of your second 10 flips to be a head).
So that’s 1/2 for each flip, you need all 10 to match, so we have (1/2)^10 = 1/1,024
If ordering doesn’t matter – say you had 5 heads in the first, you need 5 heads in the second, this becomes a bit more awkward. I’m going to say… it is the sum of the probability of all ways of doing this (so 10 heads and 10 heads, plus 9 heads and 9 heads, plus…). If my numbers are correct I get 17.6%, or about one in 5.7 for that.
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