Katydid School
The answer is yes, it is to your advantage to switch. When the three boxes
all hide their contents, there is a 1 in 3 chance that any one
of them contains the car. If you select a box, then there is a 1 in 3
chance that your box contains the car, and a 2 in 3 chance that
one of the other two boxes contains the car. (Note that there is also a 100%
chance that at least one of the other boxes contains a goat.)
Now, when Monty exposes a goat from the group of two boxes, he is not
altering odds associated with the group: it was always known that at least
one of the boxes had a goat in it, Monty just exposed it, that's all.
The group of two boxes originally had a 2 in 3 chance
of having the car in it (even
though at least one of the boxes was guaranteed to contain a goat), and those
odds remain with the other box since it came from a larger selection group.
Since the odds of the other box are 2 in 3 to contain the car, it is to your
advantage to switch.
What's that? Not satisfied? Try the
Wombat school!
The car-goat-goat Problem /
corby@intuit.com
December 1994 (updated April 6, 1998)