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Ohio Crash System

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In a certain state lottery, a lottery ticket costs $$2.$ In terms of the decision to purchase or not to purchase a lottery ticket, assume that the following payoff table applies.

State of Nature

Decision Alternatives

Win $51$

Loses $52$

Purchase lottery ticket, d$1$

$$250,000$

$-$$$2$

Do not purchase lottery ticket, d$2$

$$0$

$$0$

$($a$)$ 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 answers to two decimal places. For subtractive or negative number use a minus sign $($Example: $-300).$ If your answer is zero enter $"0".$

EV$($d$1)=$

EV$(02)=$

Recommended decision:

$-$ Select your answer $-$ v

$($b$)$ If a particular decision maker assigns an indifference probability of $0\mathrm{.}000001$ to the $$0$ payoff, would this individual purchase a lottery ticket? Use expected utility to justify your answer.

If required, round your answers to six decimal places.

EU$(01)=$

EU$($d$2)=$

Purchase a lotery ticket?

$-$ Select your answer $-$ v