TheMonty Hall problemis a brain teaser, in the form of a probability puzzle, loosely based on the American television game showLet's Make a Dealand named after its original host, Monty Hall. The problem was originally posed in a letter by Steve Selvin to theAmerican Statisticianin 1975. It became famous as a question from a reader's letter, quoted in Marilyn vos Savant's "Ask Marilyn" column inParademagazine in 1990:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No.1, and the host, who knows what's behind the doors, opens another door, say No.3, which has a goat. He then says to you, "Do you want to pick door No.2?" Is it to your advantage to switch your choice?

• Would you stay with your original door selection, or would you switch? Explain your reasoning.
• Watch the following video about the Monty Hall Problem.

Video- https://www.youtube.com/watch?v=4Lb-6rxZxx0

If you need additional explanation, you can watch these videos

https://www.youtube.com/watch?v=7u6kFlWZOWg

https://www.youtube.com/watch?v=Xp6V_lO1ZKA

or

https://www.youtube.com/watch?v=9vRUxbzJZ9Y

Indicate which videos you watched. If you found another one on your own, include the link.

What is the probability of winning if you stay with your original door selection?

What is the probability of winning if you switch to the other door, after you've been shown the door with a goat?

Write a paragraph explaining why a contestant should switch doors on the game show.

Video citations:

Numberphile (2014, May 22). Monty Hall Problem[Video]. | Youtube | 5.30 min.

Numberphile (2014, May 28). Monty Hall Problem for Dummies[Video]. | Youtube | 4.17 min.

Khan Academy (2012, Jun 27). Probability and the Monty Hall Problem [Video]. | Youtube | 7.22 mins.

AsapSCIENCE (2012, Nov 6). The Monty Hall Problem - Explained[Video]. | Youtube| 2.47 mins.