Imagine
you are on a game show
and the host displays three large boxes, one of
which contains the grand prize of a car and the
other two contain goats. You will be awarded the
contents of the box that you choose at random,
but the contents will not be immediately revealed.
After you make your choice known, the host
opens one of the other two boxes and reveals a
box with a goat. The host then asks if you would
like to switch your chosen box for the remaining
unopened box.
The scenar io is from a notable statistical
game known as the Monty Hall Problem. This
mat hemat i ca l p rob l em i s s imp l e enough
to under stand, but the answer is somewhat
counter intuitive. What would you do in thi s
scenar io? Would you stick with your or iginal
choice or would you swap? Which would make
more sense in giving you a higher chance of
winning the car? When this problem was released
in a magazine back in the 70s, most believed
that it made absolutely no difference whether
you swapped or stuck to your choice, and that
the chance to win the grand prize stayed at 50%
either way. Intuitively sensible – but statistically
incorrect.
The mathematics reveals that swapping nearly
doubles the chance of winning the grand prize.
However, it should be noted that this is only true
when the following 3 conditions are met [1]:
(1) The host does not reveal the original choice;
(2) The host always opens a box containing a
goat (we are assuming that he knows what
each box contains);
(3) The host makes a random choice of boxes
to open, when your initial choice was
correct.
When you are asked to pick a box at the very
beginning, the probability of selecting the grand
prize is one out of three (1/3). The probability
of picking a goat is 2/3. If you do not decide
The Monty Hall
Probabili
This article may be useful as supplementary reading for mathematics classes, based on the DSE syllabus.
