[_urga]

"If you flip a fair coin 1,000,000 times and get 1,000,000 heads in a row, the probability of getting heads on the next flip is still 1/2."

Does this square with the law of large numbers? The example is almost loaded to begin with, only claiming "a fair coin" but then going out of the way to show the opposite.

I would give the author the benefit of the doubt, but I would have thought a more accurate definition would be that the average outcome for many coin flips would be heads 50% of the time, given enough flips and assuming a fair coin.

So seeing 1,000,000 heads in a row, after 1,000,000 flips, would make me think the probability of heads the next flip is actually 100%, because this coin obviously is not fair.

Technically, if the coin is known to be fair, then sure...

[shoemakersteve]

I think that was the point. They're trying to say that if, hypothetically, you knew the probability was 1/2, and you flipped it a million times and only got heads, the probability doesn't change. The law of large numbers doesn't say this is impossible, just that it's incredibly, incredibly unlikely.

[lakis]

I would say that after 1M times of heads in a row, the probability of getting a head is very close to 1 because there is a 0.9999999999999% chance that this coin is not fair and will always come head. I understand that mathematically the probability is 1/2. But in real life, there is a higher chance that the coin is biased somehow