Introduction

"Heads, you go first; tails, I do."

"I need to roll a seven to win."

How many times have you played a game and hoped to win? What is the probability of winning? The purpose of this WebQuest is to introduce you to some interesting problems and learn about probable outcomes. At the conclusion of the WebQuest you will be able to explain why some choices are better than others.

Task

Your task is to solve and analyze several problems about probability. After you have completed this task and understand how probability works, you will answer several critical thinking questions. Your final project will include:

· A tally sheet showing the results of coin flipping

· Answers to the questions on independent events

· A printed copy showing your results while playing one of the Monty Hall simulation games

· An explanation about whether or not you should switch your door selection during the Monty Hall game

Process

1. Predict how many times a coin will land heads up or tails up when flipped 50 times.

Flip a coin 50 times. Tally the heads and tails in the worksheet provided. How close was your prediction? Compare your results with those of your classmates.

2. Investigate how to calculate independent events. Choose one of the following websites to read. Then answer the questions on your worksheet.

Websites for learning about Independent Events:

http://www.mathgoodies.com/lessons/vol6/independent_events.html

http://argyll.epsb.ca/jreed/math8/strand4/4203.htm (scroll down about half the page)

3) There used to be a game show in the 1960’s called “Let’s Make a Deal.” Here is the Opening Line:

"Would you make a deal to trade up to five hundred dollars in cash for one of these three doors, knowing behind one of them is $3,254 in cash or valuable merchandise? Several people may have to make that decision during the next few minutes as we bring you the Marketplace of America.... Let's Make a Deal! And now, here's America's top trader, TV's Big Dealer, Monty Hall!

The well-known Monty Hall probability problem is based on a television show of the 1960's and 1970's called Let's Make a Deal. Show host, Monty Hall would ask a contestant to pick one of three doors. Behind one of the three doors was a large prize. Behind the other two doors were lesser prizes, sometimes a group of goats grazing on fresh hay. J

Once the contestant picked a door, Monty would open one of the remaining two doors that did not have a prize. Then, he would offer the contestant a chance to switch doors.

Try one of the Monty Hall simulation games listed below. Remember that you have already made a prediction as to whether or not it is better to switch door selections after one is revealed. Tally your results either on the Web or on the Monty Hall Tally Table. (If you tally the results on the Web, be sure to print them out.) What happened? Compare your results with those of your classmates.

Websites for the Monty Hall Simulation:

Monty Hall Simulation
http://math.ucsd.edu/~crypto/Monty/monty.html

Monty Hall, Three Doors (Two Simulations)
http://www.shodor.org/interactivate/activities/monty3/

Evaluation

4. Answer the critical thinking questions on the worksheet. They will be graded using the following rubric:

1 2 3 4

Faulty reasoning or no evidence of reasoning.

Some evidence of mathematical reasoning appropriate to problem.

Uses effective mathematical reasoning.

Employs refined and complex reasoning with no mathematical errors.

Mathematical

Reasoning