Algebra 2 Challenge Problem 3

Due by 10AM Monday 10/15 via email

 

There is a new one time game show called pick the Bugatti Veyron (the only street legal car in the world with > 1000 horsepower).  There are 100 doors, and only one door has the car.  To start the game you pick a door.  The game show host, who knows where the car is, opens the remaining doors that do NOT have the car one by one.  When 98 doors without the car have been opened by the game show host, she asks you a question:

"Do you want to keep your current door or do you want to switch?" 

a)  What is the likelihood that your door holds the car if you do NOT switch? 

 

b)  What is the likelihood that your door holds the car if you do switch? 

 

c)  Based on your answers to parts a) and b), should you switch or not?

 

Explain all your answers.