Transcript Slide 1

The Monty
Hall
Problem
Probability and Statistics
•Probability Theory
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

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
The big question….
Should you
switch???
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
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
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!
References
http://math.ucsd.edu/~crypto/Monty/montybg.html
https://www.khanacademy.org/math/trigonometry/prob_c
omb/dependent_events_precalc/v/monty-hall-problem
http://en.wikipedia.org/wiki/Monty_Hall_problem#Solution
s