Puzzle: The Monty Hall Problem

"Ask Marilyn” is a famous column where Marilyn answers readers’ questions. (Marilyn is listed as the world’s highest recorded IQ: 228). One of the questions was inspired by the game show “Let’s Make Deal” hosted by Monty Hall.

In the game, there are 3 doors with 2 goats and 1 car. You start by choosing one door; the host then opens of the “goat” doors. You are now left with 2 doors. The host asks if you would like to switch the door? 

Is it better to switch or not?

You would think that it makes no difference. Marilyn said that it is better to switch. Almost 10,000 readers of which are 1000 PhD holders were upset with Marilyn’s answer. One of them even said, “If all those PhD holders are wrong then the country is in serious trouble”! but at the end Marilyn was right J

Easy Explanation     

Scenario One: You are lucky, you choose the door with the car and you win (probability: 1/3)

Scenario Two: You are not lucky (probability 2/3), you choose the door with the goat, at this point the host opens the “goat” door, and hence you are left with the “car” door and so it’s better to switch.

Door 1	Door 2	Door 3	result if switching	result if staying
Car	Goat	Goat	Goat	Car
Goat	Car	Goat	Car	Goat
Goat	Goat	Car	Car	Goat

The table is taken from the Wikipedia

Which clearly shows that if you switched, the chance of getting the car would be (2/3 or 66%) while if you didn’t switch, the chance of getting the car would be (1/3 or 33%)

Does it make sense? J

Source: Book: The Drunkard's Walk: How Randomness Rules Our Lives