The Monty Hall Problem

1. The Monty Hall Problem • Probability and Statistics • Probability Theory

2. History • September 1991, a reader of Parade asked a question to the “Ask Marilyn” column • If you’re on a game show and you can choose one of three doors where there’s a car behind one and a goat behind the other two, after picking a door, would you switch doors after being revealed one with a goat? Is there an advantage? • Marilyn Vos Savant responded saying it would be better to switch, and there was a lot of controversy with this response • Matthew Carlton, Cecil Adams, and Keith Devlin later gave their reasoning that aligned with Marilyn’s

3. History cont’d • This dilemma was named after Monty Hall • Monty Hall was the host of Let’s Make a Deal in the 1960s and 1970s • 3 doors are shown and the contestant picks one • One door has a car, the other two have nothing • A door that wasn’t picked is opened to reveal it’s empty • The contestant has a choice to stick with their door or change to the other one

4. The big question…. Should you switch???

5. Explanation • The choice isn’t luck but based on probability • 1/3 chance of picking the car at the beginning • Once a door is eliminated, the chance of winning a car between the last 2 doors is NOT 50-50 • Need to look at 2 options: • Always switching • Always staying

6. Explanation Cont’d • Always stay: • 2/3 chance of picking a door with nothing • 1/3 chance of picking the door with the car • Always switch: • 2/3 chance of picking a door with the car • 1/3 chance of picking a door with nothing

8. There is a 2/3 chance of getting the car if you switch. This means you have a better chance at winning if you switch!

9. References http://math.ucsd.edu/~crypto/Monty/montybg.html https://www.khanacademy.org/math/trigonometry/prob_comb/dependent_events_precalc/v/monty-hall-problem http://en.wikipedia.org/wiki/Monty_Hall_problem#Solutions