• So, should you stick with your original choice or switch your choice?
  • Switch! You have a 66% chance of getting the good gift.
    • There are two goats, three choices—you have a 66% chance of originally choosing a goat.
    • So, it’s most likely that you’ve chosen a goat when Santa (or Monty Hall, or Wayne Brady, see below) reveals a goat behind a different door.
    • Since it’ shots likely you’ve chosen one goat and the other one is revealed, make the switch! You have a 66% chance of getting the good gift.

• Why is it called the Monty Hall Problem? Was Monty Hall a famous mathematician?
  • No, he was a game-show creator and host. His show, Let’s Make a Deal, frequently hid three prizes (two goats, one car) behind three doors. Let’s Make a Deal is hosted by Wayne Brady these days, and contestants still face the Monty Hall Problem on a daily basis.

• Try the Monty Hall Problem with your class or family this holiday season.
  • Hide two give-away gifts and one swanky one in similar boxes.
  • Have a student or family member choose a gift.
  • Before revealing the gift they chose, reveal one of the (unchosen) give-away gifts.
  • Give the person the opportunity to change their answer.
  • Reveal the gifts!
  • What are the statistics for choosing a good gift when you switch your original choice? Do your statistics change the more often you play?

TEACHERS’ TOOLKIT

Vox: The Monty Hall Problem video

Nat Geo: World Statistics Day