Suppose you’re a contestant on Let’s Make a Deal. Monty Hall shows you three doors. One hides a sports car; the other two hide goats. You choose Door #1.
Before opening Door #1, though, Monty opens Door #3, revealing a goat. Now you can stick with Door #1 or switch to Door #2. Which should you do?
|
SelectClick for Answer |
You should switch to Door #2.
At the start, each door had a one-third chance of hiding the car. You chose Door #1, accepting a two-thirds chance that the car was really behind Door #2 or Door #3.
In revealing the goat behind Door #3, Monty has helped you by removing that door from contention. Therefore the two-thirds chance now rests entirely with Door #2.
This is counterintuitive, but it’s true. If you picture the universe of possibilities, you’ll see that in two-thirds of the cases you initially pick a goat, and Monty shows you where the car is by revealing the other goat. Only in one-third of the cases will you pick the car correctly on the first move, when switching is a bad idea.
|
