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Another tricky question is the one about 3 doors, two with goats behind them, and the 3rd one is hiding the prize. The host opens door #1 with a goat behind i

by pajko 3y ago

Another tricky question is the one about 3 doors, two with goats behind them, and the 3rd one is hiding the prize. The host opens door #1 with a goat behind it, the doors #2 and #3 are still closed. Now what's the chance of the door #2 hiding the prize behind it? The intuitive answer is 50%, but it's wrong.

anamexis 3y ago
You're not fully describing the Monty Hall problem - as you've described it, the answer is indeed 50%. In the Monty Hall problem: 1. You pick one of three doors. 2. The host opens one of the two doors you didn't pick to reveal a goat 3. You are given the opportunity to keep your original choice, or pick the other unopened door In this situation, there is a 1/3 chance that the prize is behind the original door, and a 2/3 chance it's behind the remaining unopened door.
xiande04 3y ago
That's not how it goes. And, yes, the answer is 50% in this case. The problem relies on first choosing a door (1). The host then opens a door that you did NOT choose (3) and asks if you want to switch your choice to door #2. In this case, the probability that the goat is behind door 2 is not 50%. https://en.wikipedia.org/wiki/Monty_Hall_problem https://en.wikipedia.org/wiki/Monty_Hall_problem
mlajtos 3y ago
You described a slightly wrong Monty Hall problem [0]. When I explain solution to this problem, I always just add more doors. 1 million doors, 1 car, 999999 goats. You pick one door, and I show you 999998 goats. Only two doors are left. What is the chance you picked car at the first guess? 0: https://en.wikipedia.org/wiki/Monty_Hall_problem https://en.wikipedia.org/wiki/Monty_Hall_problem
contravariant 3y ago
The answer is 0 because the prize is behind the third door #3, but I feel you're either missing a couple of details or you're trying to mess with people who know Monty-Hall.
vezuchyy 3y ago
That's still 50% though, now if you have decided to open door #2 before host opened #1 you may increase your chances by changing to door #3. The chances of a price being behind either door are exactly 50/50, it's the chance of you made the right choice in the beginning is only 33%. That is called Monty Hall PARADOX for a reason.

by pajko 3y ago

anamexis 3y ago

You're not fully describing the Monty Hall problem - as you've described it, the answer is indeed 50%. In the Monty Hall problem: 1. You pick one of three doors. 2. The host opens one of the two doors you didn't pick to reveal a goat 3. You are given the opportunity to keep your original choice, or pick the other unopened door In this situation, there is a 1/3 chance that the prize is behind the original door, and a 2/3 chance it's behind the remaining unopened door.

xiande04 3y ago

That's not how it goes. And, yes, the answer is 50% in this case. The problem relies on first choosing a door (1). The host then opens a door that you did NOT choose (3) and asks if you want to switch your choice to door #2. In this case, the probability that the goat is behind door 2 is not 50%. https://en.wikipedia.org/wiki/Monty_Hall_problem https://en.wikipedia.org/wiki/Monty_Hall_problem

mlajtos 3y ago

You described a slightly wrong Monty Hall problem [0]. When I explain solution to this problem, I always just add more doors. 1 million doors, 1 car, 999999 goats. You pick one door, and I show you 999998 goats. Only two doors are left. What is the chance you picked car at the first guess? 0: https://en.wikipedia.org/wiki/Monty_Hall_problem https://en.wikipedia.org/wiki/Monty_Hall_problem

contravariant 3y ago

The answer is 0 because the prize is behind the third door #3, but I feel you're either missing a couple of details or you're trying to mess with people who know Monty-Hall.

vezuchyy 3y ago

That's still 50% though, now if you have decided to open door #2 before host opened #1 you may increase your chances by changing to door #3. The chances of a price being behind either door are exactly 50/50, it's the chance of you made the right choice in the beginning is only 33%. That is called Monty Hall PARADOX for a reason.