It might be helpful to extrapolate this out into a higher number of doors. Say there are 10 doors instead of 3, with still just the one prize. So instead of a 33% chance of getting the right answer off the bat, you have a 10% chance.
Now, after making your choice, Monty, being the good guy that he is, opens 8 of the doors that contain no prize, leaving only the door you picked, and one other closed door. Originally, your chance of getting the right door was 10%. However, that’s just because you didn’t know what was behind the other doors. Now, you know what was behind the other doors. Now, the number of doors that could contain the prize has shrunk from 10 to 2.
The prize is definitely behind one of the 10 doors. It could be behind the one you picked at random at the start. But that only occurs 10% of the time. 90% of the time, it’s behind one of the other doors, and Monty has just shown you which of those doors it is by eliminating the other 8 possibilities. So 10% of the time, if you stick with your original choice, you’re going to get a prize. But 90% of the time, you won’t. So it’s way better to switch when given the opportunity.
Thing referenced being the Monty hall problem. Old game show would have a prize and 2 goats behind doors. You pick one then, 1 of the goats were revealed. You get the option to swap your choice
You switch because new information has been added… If the host didn’t reveal what was behind one of the doors, you wouldn’t switch (or do, it wouldn’t matter the chances are the same).
Host shows you something that removes things from the table… And that impacts the probabilities.
ponder on the fact that the host is not just opening one of the doors you didn’t pick at random, they are specifically opening one you didn’t open and that had the inferior prize. this reveals new information. if you did choose one of the two bad prizes initially (a two in three chance, right?), then the one that you can switch to must have the good prize.
I’ve never understood the logic behind switching.
It might be helpful to extrapolate this out into a higher number of doors. Say there are 10 doors instead of 3, with still just the one prize. So instead of a 33% chance of getting the right answer off the bat, you have a 10% chance.
Now, after making your choice, Monty, being the good guy that he is, opens 8 of the doors that contain no prize, leaving only the door you picked, and one other closed door. Originally, your chance of getting the right door was 10%. However, that’s just because you didn’t know what was behind the other doors. Now, you know what was behind the other doors. Now, the number of doors that could contain the prize has shrunk from 10 to 2.
The prize is definitely behind one of the 10 doors. It could be behind the one you picked at random at the start. But that only occurs 10% of the time. 90% of the time, it’s behind one of the other doors, and Monty has just shown you which of those doors it is by eliminating the other 8 possibilities. So 10% of the time, if you stick with your original choice, you’re going to get a prize. But 90% of the time, you won’t. So it’s way better to switch when given the opportunity.
Does that make it any clearer?
What do you mean prize? This image is about not murdering your fellow humans and nothing more. This explanation only raises further questions!
Thing referenced being the Monty hall problem. Old game show would have a prize and 2 goats behind doors. You pick one then, 1 of the goats were revealed. You get the option to swap your choice
Yes I know, I posted / made the image in OP
So essentially like this:
Original door has 33% chance of being good, compared to 66% chance of the other 2 doors
One of other two doors are opened by Monty, because he’s a swell guy!
The two doors still have a 66% chance of being good, but since one of them is now opened, that 66% chance now only applies to the one other door
Ergo there’s a 66% chance that if you switch doors, you’ll pick the right door
This is a great explanation. I’ve always had a hard time explaining it but I feel like changing it from 3 to 10 makes it way more obvious.
You switch because new information has been added… If the host didn’t reveal what was behind one of the doors, you wouldn’t switch (or do, it wouldn’t matter the chances are the same).
Host shows you something that removes things from the table… And that impacts the probabilities.
ponder on the fact that the host is not just opening one of the doors you didn’t pick at random, they are specifically opening one you didn’t open and that had the inferior prize. this reveals new information. if you did choose one of the two bad prizes initially (a two in three chance, right?), then the one that you can switch to must have the good prize.
First choice: you have 1 out of 3 chances to get it right
After you pick one, they eliminate another, so the one you currently have chosen is still 33% likely while the last remaining door became 50% likely
Which makes zero sense.
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