this post was submitted on 11 Feb 2024
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Showerthoughts
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A "Showerthought" is a simple term used to describe the thoughts that pop into your head while you're doing everyday things like taking a shower, driving, or just daydreaming. The best ones are thoughts that many people can relate to and they find something funny or interesting in regular stuff.
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Humans are bad at statistics and probability. We're naturally wired to find patterns and connections and make decisions quickly without needing to perform calculations. It works for simple stuff but when things get a little complicated our "gut feeling" tends to be wrong.
My other favourite probability paradox is the Monty Hall Problem. You're given the option to pick from 3 doors. Behind 2 of them are goats and behind 1 is a new car. You pick door #1. You're asked if you're sure or if you'd rather switch doors. Whether you stay or switch makes no difference. You have a 33% chance of winning either way. Then you're told that behind door #2 there is a goat. Do you stay with door #1 or switch to door #3? Switching to door #3 improves your odds of winning to 66%. It's a classic example of how additional information can be used to recalculate odds and it's how things like card counting work.
After you find out there's a goat behind door #2, you have a 50% chance whether you stay on 1 or move to three. There are only two possible outcomes at that point (car or goat), so either way it's a coin flip.
You're incorrect. It is indeed a higher chance to switch from #1 to #3. You should look up Monty Hall paradox. It's in the link that you replied to that explains it.