Understanding expected value

Read the following article, which introduces the concepts of expected value and optimal decision making. Then answer the question that follows.

EXPECTED VALUEAND OPTIMAL DECISION MAKING, BY THEAPLIAECONOMICS CONTENT TEAM

As an alternative to raising property taxes in order to increase revenue, the village of Port Chester, New York, recently increased parking meter rates by $25\%$ and also raised parking fines. According to an article from the

lohud.com news site $($Gabriel Rom, "Port Chester Increases Parking Costs, Fines,"

lohud.com, May $2,2017),$ officials are hoping that the increased parking costs will yield an additional $$500,000$ in revenue for the village. Although in the past drivers may have been more willing to risk parking illegally, the optimal behavior for Port Chester drivers may have changed as the cost of a ticket has risen.

Undoubtedly, some motonists will continue to take certain "gambles," perhaps risking a ticket for illegal parking in exchange for the benefit of saved time. Is this behavior rational? Economists analyze decisions involving uncertainty using the concept of expected value to determine optimal courses of action.

Suppose you pay $$50$ to enter into a raffle with a $$1,000$ prize. If you have a $3\%$ chance of winning, the expected value of buying a raffle ticket is