# Math Help - Monty Hall question

1. ## Monty Hall question

There are three doors and one of the doors with a goat are removed. Which of the two remaining doors should you choose to have a higher chance of getting the car?
There are ten doors and eight of the doors with goats are removed. Which of the two remaining doors should you choose to have a higher chance of getting the car?
There are two doors. Which of the two doors should you choose to have a higher chance of getting the car?
Are all of these the exact same version of the Monty Hall problem?
If so, I don't understand why it's not 50/50 in all cases.
If not, I don't understand how these are any different from the Monty Hall problem.

2. ## Re: Monty Hall question

The first is the original "Monty Hall" problem (Monty Hall being the emcee of the television game show "Lets Make A Deal"). The second is, of course, the same with the number of doors being the different. The last, I would say, is NOT a "Monty Hall" problem because "Monty Hall" doesn't do anything. The third is just a choice between two things.

However, all three leave the contestant in the same position when he makes the final decision- there are two doors, one of which has the prize behind it. The contestant has no knowledge that would make the prize more likely to be behind one door rather than the other so the two are equally likely to have the prize. The probability, as far as the contestant is concerned, that the prize is behind one specific door is 1/2= .5.

3. ## Re: Monty Hall question

The Monty Hall problem I read has the contestant choose a door before removing the goats. The questions I posted do not have the contestants choose beforehand, rather the goats are removed first before they make any decision. Does this change anything?

4. ## Re: Monty Hall question

Assume you always switch. For the three-door case, you win the car if and only if you originally pick one of the wrong doors (b/c the host will reveal the other wrong door, switching wins). You have a 2/3 chance of originally picking the wrong door.

5. ## Re: Monty Hall question

Originally Posted by daigo
The Monty Hall problem I read has the contestant choose a door before removing the goats. The questions I posted do not have the contestants choose beforehand, rather the goats are removed first before they make any decision. Does this change anything?
No, you have just stepped past the first part of the "Monty Hall problem".