A famous controversy about a probability question erupted over an item in the "Ask Marilyn" column in Parade Magazine, 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?
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Many people mistakenly believe that it doesn't matter whether you switch or stay with your original choice, as there are only two doors left and the odds seem to be 50/50. However, the correct answer is that it is actually to your advantage to switch doors.
When you initially picked a door, the probability of picking the car was 1/3. After the host reveals a door with a goat behind it, the probability that the car is behind one of the two remaining doors is now 2/3. This means that by switching doors, you have a 2/3 chance of winning the car, compared to just a 1/3 chance if you stick with your original choice.
This paradoxical result has sparked much debate and controversy, with many people refusing to believe the mathematically correct answer. Marilyn Vos Savant received thousands of letters from readers explaining why they believed she was wrong, but she stood by her answer and the logic behind it.
In conclusion, when faced with the Monty Hall Problem, it is always advantageous to switch doors to increase your chances of winning the prize.
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