For a multistate lottery, the following probability distribution represents the

Question

For a multistate lottery, the following probability distribution represents the cash prizes of the lottery with their corresponding probabilities 0.00000000801 0.00000035 0.000001548 0.000143003 0.003841104 0.007491799 0.01661155 0.97191063799 Grand prize 200,000 10,000 100 4 (a) If the grand prize is $15,000,000, find and interpret the expected cash prize. If a ticket costs $1, what is your expected profit from one ticket? The expected cash prize is (Round to the nearest cent as needed.) What is the correct interpretation of the expected cash prize? o A. You will win $0.33 on every lottery ticket O B. On average, you will win $0.33 per lottery ticket. ° C. On average, you will profit $0.33 per lottery ticket. The expected profit from one $1 ticket is S (b) To the nearest million, how much should the grand prize be so that you can expect a profit? Assume nobody else wins so that you do not have to share the grand prize (c) Does the size of the grand prize affect your chance of winning? Explain 0 A. Yes, because your expected profit increases as the grand prize increases O B. No, because the expected profit is always $0 no matter what the grand prize is ° C. No, because your chance of winning is determined by the properties of the lottery, not the payouts

Explanation / Answer

from above:

therefore expected cash prize =$0.33

option B) on average you will win $0.33 per lotter ticket

expected profit =0.33-1 = - $0.67

b) 100 million ( arond for 99 million no profit no loss)

c) option C is correct

x P(x) xP(x) 15000000 0.00000000801 0.12015 200000 0.00000035 0.07 10000 0.000001548 0.01548 100 0.000143003 0.0143 7 0.003841104 0.026888 4 0.007491799 0.029967 3 0.01661155 0.049835 0 0.97191063799 0 total 0.32662

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