Probability Brainteaser - have I got this right?

Factual Questions
1

I remember reading a brainteaser that had a counter-intuitive answer. I also remember it being discussed and confirmed in a Statistics class at one stage. I think I have the question right but I’m not sure.

Can someone please either confirm for me, or correct me on the following:

A quizmaster presents a contestant with three doors, behind one of which is a prize. The contestant chooses door A. The quizmaster, building the suspense, opens door B to reveal the prize is not there. He then askes the contestant if he wants to change his answer. The question is, should he?

The answer as I recall is that he actually has a materially greater chance of success if he does change his answer to door C. Something I think about conditional probabilities, but I can’t remember the details.

Now, I know it’s a little counter intuitive, but so is the fact that if you toss a coin and get “tails” 50 times in a row, the chances of getting tails again is still .50

Can anyone refresh me on if I’ve got the doors problem right?

Thanks so much.

M

2

Do a search on the board for “Monty Hall” and you’ll find more discussion then you care to read about this question.

3

Lovely! Thanks for the quick response.

Question closed.

M

4

BACI
Here are 2 good links:

The second link has even more links within that.

As I’ve said before, there should be about a dozen or more SDMB pages with definitive explanations for recurring topics such as:

Where’s the missing dollar?
The 3rd word ending in ‘gry’.
Does .999… really equal 1? (Yes it does !!!)
Page of collective nouns (murder of crows, etc)
Page of collateral adjectives (dog = canine; rain = pluvial, etc)

5

Since this one’s been done to death, and the links are there, let’s close this.

samclem GQ moderator