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