Monty Hall Problem

Probability Level 1

Monty Hall invites you to his show. He shows you a fiery red sports car (A Ferrari 360 Spyder!) & two goats. He hides these things behind the doors numbered 1 , 2 1, 2 & 3 3 . He now asks you to choose one of these three.

Suppose you choose Door 1 1 . Now Monty Hall shows you Door 2 2 . It contains a Goat! He then gives you two choices - stay with Door 1 1 or to switch to Door 3 3 .

If you want to maximize your chances of winning the Ferrari in the long run , what would you choose?

Image Credit : Numberphile
Take Door 2 2 Switch Stay You won't play his game

Ameya Salankar by Ameya Salankar , 23, India

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5 solutions

Did you know that there is a full website about it?

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Aneesh Agrawal
May 30, 2014

Initially all the options had 33% probability so when I chose door 1. Ye probability of other two doors were 66% When door 2 was opened it was eliminated.. So by switching I had 66% probability instead of 33% :)

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Why not 50%?

Cyd Redelosa - 6 years, 11 months ago
Ameya Salankar
May 30, 2014

You can see this for an easy understanding.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Either one, door 1 or door 3 could contain the ferrari. The probability is the same, isn't it?

Siddharth Gopujkar - 6 years, 11 months ago

The most funny thing about this problem is there was a option - " Take door 2" .. :D

Himanshu Arora - 6 years, 11 months ago
B D
Dec 21, 2018

Relevant wiki: Monty hall problem

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Max B
May 30, 2014

But the options were made so easy to guess......this is is a great problem.....but you should have made it a bit tougher

0 Helpful 0 Interesting 0 Brilliant 0 Confused

@Max B How?

Ameya Salankar - 7 years ago

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