Math 4: Probability Distributions

Colors	Count	Experimental	Theoretical
Blue	30	30%	30.83%
Pink	4	4%	2.5%
Gray	34	34%	31.67%
Orange	2	2%	1.67%
Green	26	26%	28.89%
Red	4	4%	4.44%
Totals	100	100%	100%

Part two: Expected Value

1. Find theexpected value of your repeated experiment above.
2. The context of a situation can still use expected value, but not have explicitly labeled "probabilities." For example, consider this from the course syllabus for your class:

	Tier 1	Tier 2	Tier 3
Quarter Grade	15%	35%	50%

If a student has done all Tier 1 assignments (100 Tier 1 avg), has a 80 Tier 2 average, and 65 Tier 3 average, what is the student'sexpected value? Show all calculations that lead to your answer.

1. .Create a probability distribution for an "unfair game." Show that the expected value of your game is not zero, and who the game favors (the player or the house).
2. Speaking of winning and losing, say that the game from the notes is played 100 times.

"Consider the following game. A fair die is rolled. If you roll an even number,

you lose $1. If you roll a 1 or a 3, you win 50 cents. If you roll a 5, you win $2."

1. How many times would you expect to win the game?
2. What is the probability you would win the gameexactly 40 times out of 100 plays?

What is the probability you would win the gameup to 40 times out of 100 plays? How do you know?