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Cake day: June 13th, 2023

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  • mozingo@lemmy.worldtoWikipedia@lemmy.worldMonty Hall problem
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    6 days ago

    So in the simple version where the host doesn’t do anything, there’s 3 possibilities for the car. It’s either behind door number 1, 2 or 3. So when you pick one, there’s a 1 in 3 chance you pick the door with the car.

    Now as for why the host’s choice matters: The host always opens a door that you didn’t choose and that also does not have the car. This information seems like the useful part, but it’s actually not. No matter which door you pick, one of the other two will always have a goat. He’s just showing it to you for the show, but that doesn’t change anything, because you don’t get to pick which of the two other doors, only “switch,” that’s the important part. This recontextualizes the choice you made, effectively your choice is now between the door you picked, or the other two doors combined (the one he showed you which is wrong, and the other one).

    When you first picked the first door, the odds of the car being behind it were 1 in 3, and those odds still haven’t changed. There’s still a 1 in 3 chance that your door has the car behind it. And when you first picked, there were 2 in 3 odds that the car was behind one of the two doors that you didn’t pick. Having the incorrect door revealed after the fact doesn’t change that fact about both doors. So now the door you chose initially has 1 in 3 odds and the other choice - switch to both doors - has 2 in 3 odds. That’s twice the odds, so you should definitely switch. You’ll be wrong 1/3 of the time, but it’s the best pick.

    At least that’s how I think about it: by staying, it’s like you only got to open one door, and by switching it’s like you get to open both of those two doors.

    If the host showed you the wrong door ahead of time, you’d be right though. Your choice would be between two doors and be 50/50, but by showing it after you’ve already picked one, the likelihood of the car being one of the doors you didn’t pick stays the same, and since the revealed door now has a 0 in 3 chance the last door must have that remaining 2 in 3.





















  • During the state of the union address, Donald Trump made a 13yo, who beat brain cancer, an honorary member of the secret service. It was one of many emotional plays he made to make Democrats look bad for not cheering and standing and clapping like the Republican half of the room. He made multiple jabs at democrats for not applauding things he was doing.

    So obviously it all feels like pandering and emotional manipulation when he’s also out there cutting Medicare/Medicaid and making things harder for people who are fighting things like brain cancer.