Suppose you were a contestant on
"Let's Make a deal the old television
show. The host, Monty Hall, Presents three
doors. One hides a luxury car; the others
conceal scrawny goats. YOU Must choose
The odds Of winning the car are, of
course, one Out of three, so without much
thought, you pick any door. But then
Monty mischievously opens one of the
other doors, revealing a goat. Are the odd
better if you switch your choice to the
other closed door or if YOU stay with your
original selection? It seems that it doesn't
matter. After all, there are two doors left,
so the chance of your being right is one out of two.
But actually, if You switch doors, you
are twice as likely to win. This bizarre re-
sult led to such controversy - even a mis-
taken objection by the great mathemati-
cian Paul Erdos - that it became a front-
page article by John Tierney in The New
York Times in 1991.
Here's the explanation. Of Course a goat
was always behind one of the two uncho-
sen doors; Monty's act doesn't reveal any
new information. So the initial odds of one
out of three remain unchanged. But now
for the weird twist. There must be a car
behind one of the two closed doors; if the
car isn't behind one door, it's behind the
other. So if one out of every three times
the car is behind the door you've chosen,
the other two times it will be behind the
other door. This means that the odds of
finding the car behind that other door are
two out of three. As the audience might
have correctly screamed: "Switch!