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
The chance of any given coin flip landing one way is always going to be 1/2. The chance of two coin flips landing a certain way, becomes 1/2^2(1/4) three landing a certain way becomes 1/2^3 (1/8) and so on, because it’s a half chance each time, but because you need it to be the same sequence, it’s a half of another half the deeper in the sequence you go. So basically, the odds of a series of ten coin flips coming out identically becomes 1/2^10, or as already said, 1/1024
Edit: this works with other known odds as well. Say you’re playing Yahtzee. The odds of any one die coming up on any one face is 1/6. Ergo, the odds of a Yahtzee (all dice showing the same face) Is 1/6^5 (1/7776)
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%
It’s the same as any other unique set of results. Nothing statistically binds one coin flip to another. After 10 heads in a row, the odds of a heads on the next flip is still 50/50.
Thanks guys. I’m seeing people saying it’s 1/1024 with is almost .10% or one tenth of a percent. But then I see some people saying it’s 17% chance.
Just to clarify, I’m asking what’s the percent possibility that you can have the EXACT same sequence of H/T in the EXACT same order as the last 10 flips.
Would love some more clarification please. Thanks!
Latest Answers