Monty Hall Problem Simulation

Let’s Make a Deal Simulation

Does switching make any difference to the chance of winning a car?

This game is based on the old game show “Let’s Make a Deal” hosted by Monty Hall (or in its current incarnation by Wayne Brady).  At the end of the show, a contestant is given a chance to play for the big deal of the day.  Three doors are shown:  door #1, door #2, and door #3.  Behind one of the doors was the grand prize.  Behind the other doors were zonks (worthless prizes) or at least something less desirable than the grand prize.  The contestant chooses a door.  Then Monty opened one of the other doors (but never the one with the grand prize).  At this point, the contestant can stick with his current door or switch to the door that hasn’t been opened.  He wins whatever is behind his final door.

Before beginning the simulation, ask yourself: Does it make any difference to the chance of winning a car if the contestant switches or not?

Part I: SIMULATION  

Instructions: Pair up with a partner. You will be given 3 cards—one face card (the grand prize) and two non-face cards (the zonks).   One of you will act as the host.  The host arranges the 3 cards, making sure to note where each card is located.  The contestant then picks a card.  Without showing the original pick, the host shows one of the other cards (it must always be a zonk). The contestant either sticks or switches, and his final prize is revealed.  Do this 10 times and record the results in the table below.  Then switch rolls and repeat the process.

Your trials                                            Partners trials

^[1]

Combine you and your partners’ data, and fill out the tables below:

20 trials is still a small sample size.  Collect lots of trials by visiting the National Library of Virtual Manipulatives at: http://nlvm.usu.edu/ .  Select Data Analysis & Probability, grades 9 – 12.  Scroll to the bottom and select stick or switch.  

Play 10 games, sticking every time.  Then play 10 games switching every time.  Record your data below:

Now, on the left-hand side of the applet, select multiple games.  Play 100 games, sticking every time.  Then play 100 games switching every time.  Record your data below.

Finally, pool the data from the entire class (collect only the results from the last experiment). Enter your results below.

Questions:

1. What proportion of the class’s trials resulted in a win?

1. What proportion of all “switch” trials resulted in a win?

1. What proportion of all “stick” trials resulted in a win?

1. What proportion of all wins (i.e., all cars) were the result of the switching strategy?

5. What do these probabilities tell you about your intuitive answer?

6. Does switching improve your chance of winning the car? Explain your reasoning on why or why not.

[1] Frederick County AFDA Team