# How can you use probability and probability rules in arriving at the answer? What probability ideas does this demonstrate and use?

Instructions:
This is a fun assignment to do. In chapter 5 you learned about basic probability and learned about conditional probability. Now, you get to see these two in action. You may have heard of the TV game: “Let’s Make a Deal,” where at the end of the show, contestants are presented with 3 doors and they are informed that behind one of the doors is a brand-new car. So, the contestant chooses one of three doors. Then the game show host (First one was Monty Hall), opens a door and reveals a goat. Then Monty asks if the contestant wants to switch or not. So, the question is, what is the probability of winning? Should I stay, or should I switch? What would you do?

Imagine that the set of Monty Hall’s game show Let’s Make a Deal has three closed doors. Behind one of these doors is a car; behind the other two are goats. The contestant does not know where the car is, but Monty Hall does. The contestant picks a door and Monty opens one of the remaining doors, one he knows doesn’t hide the car. If the contestant has already chosen the correct door, Monty is equally likely to open either of the two remaining doors. After Monty has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. What is the probability of winning the car if she stays with her first choice? What if she decides to switch? Think about what you think the answer is: stay or switch?

1. Watch a Ted Ed video that explains the problem: “Should I stay or should I switch doors?”

2. Write a paper that includes:

a. What did you think the probability of winning the car was, before you watched the video?

b. Information from the video what the answer really is.

c. How can you use probability and probability rules in arriving at the answer? What probability ideas does this demonstrate and use? Explain and give examples. You may use other sources as well but make sure to cite them (you may want to watch the extended version of the video if you are not sure, watch the Monty Hall Problem video. (PLEASE FOCUS ON THIS ARE MORE THAN THE REST, THANK YOU)

d. Are you surprised by the answer to the question “stay or switch”? Does it make sense?

e. 2 pages long, using size 12 font, double spaced, cover page, references included.

References;
Should I stay or should I switch doors? (n.d.). Retrieved from https://ed.ted.com/featured/PWb09pny

Please use reliable source only and use as the main resource Statistics informed decisions using data 5e by Michael Sullivan III, Joliet Junior College.

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