1. Probability and Statistics
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: Always switch:
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
omb/dependent_events_precalc/v/monty-hall-problem s