7 Days of Christmas: Day 1

In the lead up to Christmas (only one week left!) I will be posting every day, explaining some of mathematics most controversial problems.

First on the list is: The Monty Hall Problem.

Let’s suppose that you’re on a game show and the host shows you three doors. Behind one of the doors is a brand new car, but behind the other two are goats. You get to pick a door, then, the host will open one of the doors you didn’t pick and reveals one of the goats.

1.png

You now have two choices:

  • Switch doors
  • Stay with the door you chose

What do you do?

Although you think to stay with the door you chose, the best strategy is to switch every time.

Why?

Let’s say you picked door #1:

DOOR #1 DOOR #2 DOOR #3 RESULT IF STAY WITH #1 RESULT IF SWITCH
Car Goat Goat Car Goat
Goat Car Goat Goat Car
Goat Goat Car Goat Car

Therefore, if you stay, you win one in three times. If you switch, you win two in three times.

If you’re still confused, watch this video.

Let me know what you think of this 7 days of Christmas idea! M x

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