Class 10: Cars and Goats

 

Discussion 1

 

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. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door.

 

Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice?

 

Discussion 2

 

Try it out, using paper cups and a penny for the car.  With your partner, do 20 trials with the switching strategy and 20 trials with the staying strategy.  Put your results on the board.

 

Journal Assignment:

Read Marilyn vos SavantŐs explanation of the Car and Goat problem on Blackboard.  Which of her two explanations is more convincing, if either? 

Explain why the correct answer is true in your own words.

 

Bonus:  Find someone who has not heard this problem and ask them about it.  Do they think it is better to switch or stay?  Try to convince them of the answer you believe is correct.  Are they convinced?  Describe the interaction. 

 

Homework Assignment 9 for Tues, Sept. 29: 

On blackboard

 

Announcements

The next quiz will be on Thursday, October 8.  It will cover normal distributions and correlation and some probability.   

 

There is a list of possible final project topics on Blackboard under Course Materials. I will ask for final project ideas in about 2 weeks, and a proposal by the end of October.