Game #1 - Let's Make a Deal

The Game:

The contestant attempts to guess which of the three doors has a car behind it.  Each of the other doors has a goat.

How the Game is Played:

1) The contestant is asked to choose one of the three doors which they think the car is behind.

2) At least one of the doors not chosen will have a goat behind it and that goat is revealed, leaving only two doors left.

3) The contestant is then given the choice of keeping the original choice of door, or switch.

What should the contestant do?

How to test Practically:

With a partner, simulate the game twenty times where the contestant always chooses NOT to switch.

Place your results in the spreadsheet supplied by your teacher.

Simulation:

Follow this link to run a program for Let's Make a Deal.

Background:

This is the famous Monte Hall Problem, from the television show.  

A version of the Monty Hall problem was published in 1959 by Martin Gardner in Scientific American, in 1965 by Fred Moseteller in an anthology of probability problems, and in 1968 by John Maynard Smith in Mathematical Ideas in Biology. Steve Selvin presented it for the first time in a game show format in The American Statistician in 1975. The problem attracted the most attention when Marilyn vos Savant wrote about its solution in her column of the Parade magazine in September 1990. Vos Savant was famous for having the world record for the highest IQ of 228, but over 1000 people with PhDs believed her solution was incorrect and wrote in to the magazine berating her correct explanation to the unintuitive problem.