Daily Discussion Thread: Mon 20 Nov 2023
Daily Discussion Thread: Mon 20 Nov 2023
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OK guys, put on your maths brains as mine is going 😵
I watched the movie 21 yesterday and one of the opening scenes is a seemingly simple probability question.
"It's a game show and there are 3 doors. Behind 2 of the doors are goats, behind 1 is a car. A lecturer acting as a game show host asks a student to choose from 3 doors. They choose door number 1. The host opens door 3 , reveals a goat, then asks the contestant if they want to keep door 1 as their choice. The student , acting as contestant says he will go with door 2 as his odds just went from 33% to 66%.
Here's where my brain went 😵.
Aren't the choosing of doors two separate events? And don't the odds go from 33% to 50%? How is it 66%?
This is called the Monty Problem. The bit possibly not explained is that in the game, the host opening the door KNOWS which door has the car, and purposely opens one that has a goat. So now you have more information. When you choose door 1 initially, there is a 33% chance of a car in it, and 66% chance of goat. So now that host has to open a door, and if you have a goat in door 1, the host only has 1 door option to open. If you have a car, they have 2 door options. So you are better off switching, because there is a 66% chance you have a goat, and the host just revealed with other door has a goat. Wikipedia has a table which makes it more intuitive to see the possibilities.
The reason is that the door that gets opened is not random, so they are not two independent events.
There is a 66% chance that one of the doors you have not chosen has the car behind it. By showing you which one of the doors does not have the car the host effectively transfers all of that 66% chance to the one door.
Edit: that means the choice should be to switch, not stay, doesn't it? Either the student was wrong to stay or I have it completely arse about.
Edit 2 - yeah, Googled to confirm, you should switch.
The student just wanted the goat
Fair enough, goats are cool.
agree
the element that is not explained is that the door the student/contestant picks is ** never ** removed, so the odds for each door is different
( I misquoted the movie, corrected now )
Oo oo oo! I just watched this recently! The Simple Question that Stumped Everyone Except Marilyn vos Savant
Um yeah. 50%
Because why?
btw, I think I am right. These are two separate events.
Because I look at it like this. There's 3 race horses and 1 gets scratched. Your chances have gone from 33% to 50% now. Odds 1 in 2 to win now.
My definition of event . The choice is the event.
I understand what the example is trying to get across they just explained it poorly. .
They are trying to explain the principle behind card counting, which is to know what cards are left in the pack and that for each event we have to recalculate the odds to better the chances of choosing correctly over many choices.
Th difference is blackjack has an element of randomness, the dealer does not choose which card will come up.
Monty Hall knows which door has the car.
That's exactly right. The example that was given isn't comparable to counting cards because it's done in a different format.
Sorry if I don't make sense because of lack of sleep.
https://youtu.be/AD6eJlbFa2I may help.
if not, you get bonus b0nE?!?