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
Consider the following 6 flip sequences:
h-h-t-t-h-h
t-h-h-h-t-h
h-h-h-t-t-t
h-t-h-t-h-t
t-t-t-t-t-h
t-t-t-t-t-t
Every single one of them has the exact same probability of occurring, 1/(2^6) = 1/64. Every single coin flip sequence of n flips has a 1/(2^n) probability of occurring if you flip a coin n times.
If you want to, you can take the time to write out all 64 possible unique sequences of 6 coin flips. Since there are 64 sequences and one of them is t-t-t-t-t-h, this sequence has a 1/64 chance. Same for t-t-t-t-t-t.
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