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
The math behind what you’re referring to is called conditional probability. So the probability “A” (that you flip 6 tails in a row) given that “B” (you already flipped 5 tails in a row) is Prob(A) / Prob(B) = 1/64 ÷ 1/32 = 1/2.
But conceptually, you just have to realize that flipping a coin is an individual event. Think of it this way… If you roll a 6 sided die, the probability of rolling an even number is also 1/2. So your odds of rolling an even number on a die and then flipping a tails on a coin is 1/4. Let’s say you roll a die and get an even number. So now that you’re about to flip the coin, do you think the roll of your die will affect the flip of your coin? Would your odds of a tails be different if you had rolled an odd number?
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