In a certain state lottery, a lottery ticket costs $4. In terms of the decision
ID: 3050199 • Letter: I
Question
In a certain state lottery, a lottery ticket costs $4. In terms of the decision to purchase or not to purchase a lottery ticket, suppose that the following payoff table applies:
A realistic estimate of the chances of winning is 1 in 200,000. Use the expected value approach to recommend a decision. If required, round your answer to two decimal places.
Recommended decision: Do Not Purchase Lottery Ticket
Expected Value = $
If a particular decision maker assigns an indifference probability of 0.00001 to the $0 payoff, suppose that the following payoff table applies:
Would this individual purchase a lottery ticket?
Decision: Yes, Purchase Lottery Ticket
Use expected utility to justify your answer. If required, round your answer to five decimal places.
Expected Utility =
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
Explanation / Answer
a)
E(X) = 1/200000 * 400000 -4 * (1 - 1/200000)
= -1.99998
E(X) < 0
hence Do Not Purchase Lottery Ticket
b)
E(X) = p U(10) + (1-p) U(0)
= 1/200000 * 10 -0* (1 - 1/200000)
=0.00005