Question5 1 pts In a particular lottery, 3 million tickets are sold each week fo

Question

Question5 1 pts In a particular lottery, 3 million tickets are sold each week for 50 cents each. Out of the 3 million tickets, 12,006 are drawn at random and without replacement and awarded prizes: twelve thousand $25 prizes, four $10,000 prizes, one $50,000 prize, and one $200,000 prize. If you purchased a single ticket each week, what is the expected value of this game to you? Round your answer to the nearest 0.0001. Question6 1 pts Suppose that a school has 20 classes: 16 with 25 students in each, three with 100 students in each, and one with 300 students, for a total of 1000 students. Select a student randomly out of the 1000 students. Let the random variable X be the size of the class to which this student belongs. Find E(X), the expected value of X Round your answer to the nearest O.0001

Explanation / Answer

Let X = prize amount in dollars.

Pr(X = 25) = 12,000/3,000,000
Pr(X = 10,000) = 4/3,000,000
Pr(X = 50,000) = 1/3,000,000
Pr(X = 20,000) = 1/3,000,000

Then the expected value of a single game to you is E[X]

=-0.50 for buying the ticket + 12000/3000000 * $25 + 4/3000000 * $10,000 + 1/3000000 * $50,000 + 1/3000000 * 200,000
= -0.50 + 1/10 + 1/75 + 1/60 + 1/15
= -0.50 + 0.10 + 1/75 + 1/12
= -0.50 + 0.10 + 29/300
~= -$0.3033

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