My Brane is Perfect

Submitted by 500poundsofnothing in just_post

last night some friends were discussing probability and I chimed in that they were doing the math wrong but it was past midnight so I wasn't sure. I eventually concede because intuition and probability don't mix especially in the early hours of the morning. This morning I wake up and set out to prove my intuition wrong via simulations and then proved myself right.

I can feel my brane pulsing with genius

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twovests wrote

I have had this interaction several times. I would love to feel your pulsing brane (that is, I would love to see your simulations / know more about the context) (I love probability, and verifying with my good pal Monte Carlo)

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500poundsofnothing OP wrote

Replying to twovests (#23,411)

A friend has a thing in a video game where she was trying to get items from a limited pool of 20 items that couldn't have any repeat and it took her 20 tries to get the item she wanted. People were saying there is a 1 in 20! chance of this happening, while I think there is just a 1 in 20 chance of this happening because while it is true that this exact permeation of events happening is 1 in 20! there are also 19! outcomes that have the same property so the chance of this happening.
My intuition was that if you had a deck of 19 black cards and 1 red card if the only information you care about is where the red card is then there is only 20 possible outcomes so the question we are asking is what is the chance that the red card is on the bottom of the deck and that is 1 in 20.

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twovests wrote

Also I think bragging about this kind of thing is cool and I want you to do it more (genuine)

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flabberghaster wrote

Replying to 500poundsofnothing (#23,412)

you're not gonna like this but you have a mathematical mind and you'd be good at programming if you wanted to do it. I'm sorry to say this. But unfortunately your ability to break down a complex problem into the most basic version and work backwards from there is a very valuable skill.

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