Monty Hall

Complementary Probability

LET'S MAKE A DEAL

Back in the old days of Let's Make A Deal, Monty Hall would show a contestant three doors. Behind two of the doors were farm animals of varying species. Behind the other door was a little red sports car with a blond of your gender preference. The contestant would guess which door veiled the prize, and Monty would open another door revealing a donkey, a goat, a sheep, or a whatever. Then Monty would ask the contestant if he or she wanted to stick or switch doors. Depending on whether the contestant stuck to the original choice, or switched to the other unopened door, he or she went home with style or sty. They just don't make TV like they use to.

DIRECTIONS

Click a door to pick a door.
Play the Monty Hall simulation above 100 times.
STICK to your original guess for all 100 times.
When you have played the 100th time, screencopy and save your results.
CAREFUL when you get to 100. The counter resets after playing 100 times.
Play the Monty Hall simulation again 100 times.
This time SWITCH each time from your original guess after Monty opens a door.
When you have played the 100th time, screencopy and again save your results.
Email both the STICK and the SWITCH copies to your instructor.
Do not use anyone else's copy,
Or you and the one you copied from will receive no points.
Now answer the questions in the table below for 10 points maximum.
After you have completed the table, screencopy it and email it to your instructor.
Due by noon one week from today.

QUESTIONS

What is the probability that you will pick the car door on your first guess?
What is the probability that you will not pick the car door on your first guess?
After Monty opens a door, what is the probability that your door conceals the sports car?
After Monty opens a door, what is the probability that your door does not conceal the sports car?
In the simulation, how many times did you win when you Stuck to your original guess?
In the simulation, how many times did you win when you Switched from your original guess?
Do these last two answers agree with your two answers to #3 and #4?
Would you like to stick with your answers to #3 and #4, or switch?
Suppose instead of three doors, there were ten doors. Suppose you guess Door #10, and Monty opens eight of the remaining doors. What is the probability that you picked the car door on your first guess?
Should you stick to Door #10 or switch?

Note that answers with numbers require 3 decimal precision.

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Last Modified 11/13/08 5:18 PM

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