Goats and Cars Quiz Puzzle Answer

This week we have quite a famous puzzle, but one that's worth sharing if you've not seen it. And it's an interesting and counter intuitive puzzle as well! 

It first came to prominence in 1990 as a reader's question to Marilyn vos Savant's column in Parade magazine:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, 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 to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?


This is loosely based on an actual game show where this was the problem given to contestants.

So, you are on the game show you are asked to pick a door. You do so and the host opens one of the other two doors to reveal a goat. You can stick with your original door or change to the other unopened door. Do you stick? Do you change? Or does it make no difference?

This is known as the Monty Hall Problem after the original host of the game show.

In the three situations below assume that you always pick door one.

  1. If the car is behind door one the host can choose which door to open to reveal a goat, and if you switch you change from the car to the other goat and lose the car.
  2. If the car is behind door two the host has to open door three to reveal a goat, and if you switch from door one to door two you win the car.
  3. If the car is behind door three the host has to open door two to reveal a goat, and if you switch from door one to door two you win the car.

These are the only three possible situations, and in two of them you win by switching. So your odds of winning by switching are 2/3 and of losing are 1/3; you should always switch.

Put another way, the only way you can lose by switching is if you picked the car in the first place, and the odds of picking the correct door from three doors is 1/3.

When this answer was published in the magazine many people refused to believe it correct. Thousand's of them wrote in to complain.

But it is correct, however counter intuitive it might seem.



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