Reference no: EM133744370

Question: A famous controversy about a probability question erupted over an item in the "Ask Marilyn" column in ParadeMagazine, written by Marilyn Vos Savant. The problem her column addressed was loosely based on a TV game show called Let's Make a Deal, hosted by Monty Hall, and hence is known as the Monty Hall Problem. Here's the question:

Suppose that you're on a game show and you're given the choice of three doors: Behind one door is a car, behind the other two doors are goats. You pick a door, say No. 1, and the host who knows what's behind the doors opens another door, say No. 3, which has a goat. He then says do you want to change your pick to door No. 2? Is it to your advantage to switch your choice?

Marilyn answered that the probability of winning was higher if the contestant switched. This answer generated many letters, including a few from mathematicians, claiming that she was wrong. Marilyn answered with the following logic. When you first pick door No. 1, the chance that you picked the one with the car is P(door 1) = 1/3. The probability that you chose a door with a goat is 2/3. When the host opens door No. 3 to reveal a goat, this does not change the 1/3 probability that you picked the right door (Door 1) in the first place. As only one other door remains (Door 2), the probability that it contains the car is 1 - P(Door 1) = 1 - 1/3 = 2/3. Therefore, it pays to switch doors. Visit a few of the many websites devoted to the Monty Hall Problem to gain some understanding of its subtleties. Do you agree with Marilyn's logic? If so, try to explain it in your own words. If not, present an alternative approach.