4 ms·
If you rolled a dice a few thousand times and found a very unlikely subsequence of length one thousand then the dice almost certainly would be unfair. You need
by ectopod 6y ago
If you rolled a dice a few thousand times and found a very unlikely subsequence of length one thousand then the dice almost certainly would be unfair. You need to spend lifetimes rolling dice to find sequences of a thousand rolls where the numbers of ones, twos, etc. are very much different from 166.
- prepend 6y ago330M people is 330k 1k samples. So there will be some in there with different clusters of race. So it is a “lifetime” of rolling dice. Given distribution of race in the US it’s like 1-4 is white, 5 is black, 6 is hispanic. And so there will be quite a few samples of a thousand that are higher than 66% 1-4. The problem is assuming that founders would have the same distribution of the population.
- ectopod 6y ago> And so there will be quite a few samples of a thousand that are higher than 66% 1-4. Yes, roughly half of them. But that's not the point. The point is that the vast majority of those will be only slightly more than 66%. You won't see huge discrepancies. Taking your example, you would expect out of 1,000 samples for about 333 to be 5 or 6. Suppose you actually got 33 (or fewer). What would be the probability? It is 7 * 10^-125. That's 0.0000000[...]000007 with 124 zeroes before the seven. 330k samples is nothing compared to that improbability. You would expect to roll dice for longer than the lifetime of the universe to see such an unlikely event. Or you might conclude that the dice aren't fair.