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Wednesday, April 09, 2008

The Monty Hall Problem

It's a game show and there are three doors to choose from, with two goats and one sports car. You select Door 1, but before you open it, the host opens Door 3 to reveal a goat. Do you stick with Door 1 or go with Door 2?

My mathematical training says you're indifferent, that the probability is 50/50 you'll get the car behind either Door 1 or 2. But I'm wrong, and the implications are poor for a number of psychological experiments performed in the past 50 years.

Follow the first link for the real probability, and try your hand at the game itself here.

Update: as reader rick reveals, it's all about timing:
in fact, monty reveals the goat *after* we made our initial choice. that is, that goat was relevant to our first choice.

in particular, when we made the first choice, what was the chance of picking the sports car? answer: 1/3

thus there was a 2/3 chance that the car was behind one of the two remaining doors.

which of those two doors? we don't know unless somebody shows us...

1 comment:

rick said...

please excuse my math-teacher tone. our mathematical training is right. the trouble is that we haven't identified the problem correctly.

to understand this problem we must consider the importance of *when* monty reveals the goat.

if monty had revealed the goat *before* we made our initial choice, then that revealed goat is irrelevant: our choice is between one door with a goat and one door with a car. our chances of picking the car are 50%. oops, but this is not the monty hall problem.

in fact, monty reveals the goat *after* we made our initial choice. that is, that goat was relevant to our first choice.

in particular, when we made the first choice, what was the chance of picking the sports car? answer: 1/3

thus there was a 2/3 chance that the car was behind one of the two remaining doors.

which of those two doors? we don't know unless somebody shows us...