Problem

1

3

2

SWITCH

STAY

History

History

You blew it, and you blew it big! Since you seem to have difficulty grasping the basic principle at work here, I’ll explain. After the host reveals a goat, you now have a one-in-two chance of being correct. Whether you change your selection or not, the odds are the same. There is enough mathematical illiteracy in this country, and we don’t need the world’s highest IQ propagating more. Shame!
Scott Smith, Ph.D., University of Florida

May I suggest that you obtain and refer to a standard textbook on probability before you try to answer a question of this type again?
Charles Reid, Ph.D., University of Florida

Maybe women look at math problems differently than men.
Don Edwards, Sunriver, Oregon

You are the goat!
Glenn Calkins, Western State College

SWITCH

STAY

Why?

1

2

3

Three possibilities

Stay

LOSE

LOSE

WIN

Probability of winning =  1/3

Switch

LOSE

WIN

WIN

Probability of winning =  2/3

Another interpretation

every pair of closed

doors has a 

2/3 chance of winning

will guess correct door 1/3 of time

best you can do staying

choose wrong door 2/3 of time

remaining door: 2/3 chance of being right

More doors

Switch or stay?

Variants

"Angelic Monty"

the host offers to switch only when the player has chosen incorrectly 

"Monty From Hell"

the host offers to switch only when the player has chosen the winning door

"Ignorant Monty"

the host opens one of the remaining doors at random 

Lesson Learned

1. utilize all information given
   
    
2. intuition is often incorrect 
3. mathematics is a way of understanding life

 "When the facts change, I change my mind. What do you do, sir?" John Maynard Keynes

Thank you