Flipping a tail is a 1/2 chance, but flipping 6 tails in a row is a 1/64, so if after flipping 5 tails, why is it incorrect to say that your chance of flipping another tail is now lower, like you’re “bound” to get a head? I know this is the gambler’s fallacy, but why is it a fallacy? I get that each coin flip is independent, but it feels right (as fallacies often do) that in consecutive flips the previous events matter? Please, help me see it in a different way.
In: Mathematics
Provided it’s a fair coin, each flip is an independent event with a probability of 50% heads, 50% tails, you are correct. The coin has no memory; it doesn’t care what happened in the previous flips.
This does mean that over a large number of trials (flips) you would expect approximately the same number of heads and tails.
This does create something of a logical paradox because, if heads is “winning” 5-0 and over time you expect equal numbers, the probability of tails appears to have to increase.
It doesn’t; it remains 50/50
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