gambler's fallacy

[onthefringe]

Interestingly, I just saw a variation posted in a math help group I'm in.

There are four doors, one of which contains a prize. You choose door A. The host opens one of the other four doors that is incorrect. If you switch to one of the two closed doors, what is the probability of success?

Assuming the host knows which doors have prizes and always opens a non-prize door, I think your chance of success goes up to 3/8.

[wareagle]

Let's calculate the odds of any given one of us actually getting onto some game show where such knowledge might be utilized.

[Liquidambar]

Interestingly, I just saw a variation posted in a math help group I'm in.

There are four doors, one of which contains a prize. You choose door A. The host opens one of the other four doors that is incorrect. If you switch to one of the two closed doors, what is the probability of success?

Assuming the host knows which doors have prizes and always opens a non-prize door, I think your chance of success goes up to 3/8.

I got 3/8 as well (which is better than the 1/4 chance if you stick with your original guess).

[onthefringe]

Interestingly, I just saw a variation posted in a math help group I'm in.

There are four doors, one of which contains a prize. You choose door A. The host opens one of the other four doors that is incorrect. If you switch to one of the two closed doors, what is the probability of success?

Assuming the host knows which doors have prizes and always opens a non-prize door, I think your chance of success goes up to 3/8.

I got 3/8 as well (which is better than the 1/4 chance if you stick with your original guess).

I'm pretty sure that if the host knows where the prize is and always opens non prize doors, your chances will always increase if you switch after he opens. The amount your chance goes up will depend on how many doors there are and how many get opened to reveal goats, but your chances are always going to go up if you switch.

[Liquidambar]

I'm pretty sure that if the host knows where the prize is and always opens non prize doors, your chances will always increase if you switch after he opens. The amount your chance goes up will depend on how many doors there are and how many get opened to reveal goats, but your chances are always going to go up if you switch.

Yes.  If there are N doors, the probability of getting the prize without switching is 1/N.  If the host opens M of the remaining doors and then you switch, the probability of getting the prize is (N-1)/[N(N-M-1)].  Thus the probability of success is greater by a factor of (N-1)/(N-M-1) if you switch than if you don't.  As long as M, the number of doors opened by the host, is >0, you are better off switching.  (And even if no doors are opened, you aren't worse off switching.)