QUESTION 1 One state lottery has 1,000 prizes of $1; 125 prizes of $10; 25 prize
ID: 3070665 • Letter: Q
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QUESTION 1 One state lottery has 1,000 prizes of $1; 125 prizes of $10; 25 prizes of $65, 5 prizes of $345; 2 prizes of $1, 120; and 1 prize of $2,300 Assume that 29,000 lottery tickets are issued and sold for $1. What is the lottery's expected profit per ticket? QUESTION 2 One state lottery has 1,000 prizes of $1; 145 prizes of $10 25 prizes of $50: 5 prizes of $340; 2 prizes of $1.130, and 1 prize of $2,500 Assume that 36,000 lottery tickets are issued and sold for $1 What is the lottery's standard deviation of profit per ticket?Explanation / Answer
Probability of each lottery ticket(Pi) is count of ticket for that price divided by total tickets issued and (Xi) is the value of corresponding price
1.
Expected revenue of ticket = sum(PiXi)
= (1000/29000)*1 + (125/29000)*10 + (25/29000)*65 + (5/29000)*345 + (2/29000)*1120 + (1/29000)*2300
= 0.3497
Expected profit per ticket = expected revenue per ticket - ticket price
= 0.3497 - 1
= - 0.6503 (Negative sign indicates loss as ticket price is more than expected return from ticket)
2.
Expected revenue of ticket = sum(PiXi)
= (1000/36000)*1 + (145/36000)*10 + (25/36000)*50 + (5/36000)*340 + (2/36000)*1130 + (1/36000)*2500
= 0.2822
Expected profit per ticket = expected revenue per ticket - ticket price
= 0.2822 - 1
= - 0.7178 (Negative sign indicates loss as ticket price is more than expected return from ticket)
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