Assignment:
Write a problem that you think would make a good exam question, give it's solution and a brief, well-written explanation of why you think it's a good exam question.


Problem:
You are a producer on the television game show, "The Price Is Right." You have been asked to redesign the 'Plinko' board from its current square design (see graphic) to a new triangle shape. The concept will remain similar to the way 'Plinko' is played now. A player will drop a chip in from the top point of the triangle and it will bounce off of a variety of spikes that are laid out in a pattern similar to Pascal's Triangle. There will be a row of containers on the base of the triangle. Depending on which bucket the chip falls into will determine how much money the contestant wins. Each bucket represents cash prizes between $25,000 and $1,000. Knowing this:

a.) Where on the base of the triangle would you place the bucket representing the $25,000 prize if your goal was to give away as much money as possible on the show? Explain why.

b.) Where on the base of the triangle would you place the bucket representing the $25,000 prize if your goal was to give away as little money as possible on the show? Explain why.

Solution:
a.) Place the $25,000 prize in the middle of the board. Based on Pascal's Triangle, there are more ways to get to the center of the base than any other place at the base of the triangle.

b.) Place the $25,000 prize at either end of the board. Based on Pascal's Triangle, there is only one way to get to the extreme sides of the triangle, which would be to follow the wall down completely.


Explanation:
We thought that this would be a good problem for the exam based on class discussion. The question will see how well students paid attention in class and will also show understanding of a core pattern in probability (and algebra): Pascal's Triangle.

Online URL: http://www.personal.psu.edu/users/b/s/bse114/ist230/hw8testquestion.html

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