A lottery sells 1 million tickets.
QUESTION
A lottery sells 1 million tickets.One of those tickets wins the grand prize of $1 million, 100 tickets win 1st place prizes of $10,000, and 10,000 tickets win prizes of $1.(a) What is the expected value of winnings from a single lottery ticket?(b) What is the variance of the winnings from a single lottery ticket?(c) If lottery tickets cost $4, should you buy one? Why? What if they cost $1?
(a) Denote the winnings from a single lottery ticket by L. A single lottery ticket pays $1,000,000 with probability 1/1,000,000, it pays $10,000 with probability 1/10,000, and it pays $1 with probability 1/100. Therefore, the expected value of winnings from a single lottery ticket equals (b) The variance of the winnings from a single lottery ticket equals c) The following argument is based on the fact that a potential buyer of a lottery ticket is risk-averse or is risk-neutral. If the ticket costs $4, its cost is higher than
the expected winnings. In this case, a risk-averse or risk-neutral person would not buy the ticket. If the ticket costs $1, its cost is lower than the expected earnings. If someone is risk-neutral or only very weakly risk-averse, this person should buy the ticket. If, however, the person is strongly risk-averse, this person should not buy the ticket.
ANSWER:
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