Monty Hall Problem

Time for a pop quiz! Say you are on a game show. You are presented with 3 different doors and are told that 2 of the doors contain goats and the 3rd door contains 6 quadrillion dollars! You are told to choose which door has the money, so you choose door number 1. At this point the game show host turns to you and says, “What a choice! Let’s look at what was behind door number 2. It was a goat! I’ll give you another chance since you know that the second door was a goat. Do you want to stay with door number 1 or switch?” What is the better choice: to stay with door number 1, to switch to door number 3, or do both doors have the same probability of having the goat/money?

Key points:

  • you choose a random door out of 3 doors (2 of which are ‘bad’ and 1 of which are ‘good’)
  • the game show host reveals that one of the other 2 doors is one of the ‘bad’ doors
  • you are asked whether you would like to keep the original door or switch
  • Which is better to stay, to switch, or are both the same chance?

This is called the Monty Hall problem because there used to be a game show back in the day that was put on by a guy named Monty Hall. I’m sure it was a super fun show!!!

[Solution after the holidays!]