3 ms·
Yes. If Monty opens the door by chance there are 3 equally likely cases: There's a 1/3 chance you picked the car and Monty shows you a goat, 1/3 chance you pic
by full_monty 3y ago
Yes.
If Monty opens the door by chance there are 3 equally likely cases: There's a 1/3 chance you picked the car and Monty shows you a goat, 1/3 chance you picked a goat and Monty shows you the other goat, 1/3 chance you picked a goat and Monty shows you a car. So if Monty shows you a goat you have equal probability of being in one of the first two cases.
If Monty doesn't open the door by chance then he never shows you a car. So 2/3 of the time you picked a goat and Monty shows you the other goat.
- krackers 3y agoYup, the fact that you only have an advantage in switching when Monty "leaks information" in explicitly choosing _not_ to open a certain door as [1] pointed out, is likely the crux of what makes this unintuitive, since it is a very unusual prior. [1] https://news.ycombinator.com/item?id=39514463 https://news.ycombinator.com/item?id=39514463