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"It's a 10% chance which I did 10 times, so it should be 100%" — LessWrong

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Many of you readers may instinctively know that this is wrong. If you flip a coin (50% chance) twice, you are not guaranteed to get heads. The odds of getting a heads are 75%. However you may be surprised to learn that there is some truth to this statement; modifying the statement just slightly will yield not just a true statement, but a useful and interesting one. It's a spoiler, though. If you want to figure this out as you read this article yourself, you should skip this and then come back. Ok, ready? Here it is: It's a 1 / n chance and I did it n times, so the odds should be... 63 % . Almost always. Suppose you're flipping a coin and you want to find the odds of NOT flipping a single heads in a dozen flips. The math for this is fairly simple: The odds of not flipping a single heads is the same as the odds of flipping 12 tails. which is The same can be done with this problem: you have something with a 1/10 chance and you want to do it 10 times. The odds of not getting it to hap

x "It's a 10% chance which I did 10 times, so it should be 100%" — LessWrong Probabilistic Reasoning Logic & Mathematics Probability & Statistics Rationality World Modeling Curated 170 "It's a 10% chance which I did 10 times, so it should be 100%" by egor.timatkov 18th Nov 2024 3 min read 61 170 Many of you readers may instinctively know that this is wrong. If you flip a coin (50% chance) twice, you are not guaranteed to get heads. The probability of getting a heads is 75%. However you may be surprised to learn that there is some truth to this statement; modifying the statement just slightly w

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