# Thread: David Spence: Monty Hall revisited

1. ## David Spence: Monty Hall revisited

Masochistic though it may be, I rewatched 21 recently. It made me think of the following variations on the classic Monty Hall problem:

1) Instead of three doors, suppose there are n doors. The host opens a door he knows to have goats. What is the probability that switching to one of the unopened doors will result in winning the car?

2) Same as above, but now the host opens a random door, not knowing whether it will reveal a goat or the car. If the host does not reveal the car, what is the probability that switching to one of the unopened doors will result in winning the car? Is it always wise to switch in this case?

2. ## Don Schlesinger: Re: Monty Hall revisited

> Masochistic though it may be, I rewatched 21
> recently. It made me think of the following variations
> on the classic Monty Hall problem: 1) Instead of
> three doors, suppose there are n doors. The host
> opens a door he knows to have goats. What is the
> probability that switching to one of the unopened
> doors will result in winning the car?

(n-1)/n(n-2)

2) Same as
> above, but now the host opens a random door, not
> knowing whether it will reveal a goat or the car. If
> the host does not reveal the car, what is the
> probability that switching to one of the unopened
> doors will result in winning the car?

1/(n-1).

>Is it always wise to switch in this case?

No. Switching doesn't help.

Don

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