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chemist612 t1_ja842e1 wrote

Probability (and science in general) hinges heavily on semantics. The chance to roll a 6 on a die never changes (1/6), but the chance of having 10 consecutive non-6 rolls is relatively low ([5/6]¹⁰=.162), so the chance of rolling exactly one 6 in a string of 10 rolls is 1-.162=0.838. So if you've had nine non-6s it feels like there is an ~84% chance of rolling a 6 on the next roll, but it is still just a ~17% chance.

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cmlobue t1_ja86wa6 wrote

0.838 is the probability of having at least one 6 among your ten rolls. You need to get into binomial distributions for the probability of a specific number of events. Exactly one six somewhere in the sequence is probability 0.323.

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chemist612 t1_ja9bm60 wrote

You are correct. I should have said at least 1 six. But the logic still holds for the types of arguments people try to make about 9 non-6s in a row, so the 10th must have a higher probability, but in-fact it doesn't.

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ShadowDV t1_ja8ztuo wrote

Had to scroll way to far to get here.

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