In a certain National Park, a pass for the day costs $20. It is possible to ente
ID: 3069002 • Letter: I
Question
In a certain National Park, a pass for the day costs $20. It is possible to enter the Park without buying a pass (there are many roads into the park, and it is impossible to post an entry station on each one), but if you are caught in the Park without a pass you will pay a fine of $500. The probability that you will be caught is 1/10. Obviously the legal, moral and honest thing to do is buy a pass without regard to the likelihood of your getting caught, but putting aside considerations of morality and honesty, and thinking purely in terms of dollars and cents, is buying the pass, on average, a wise choice? Explain. (Think in terms of expected value. If you buy a pass your EV is -20. What is your EV if you choose not to buy one?)
Explanation / Answer
Cost of day pass for entry into the National Park = $20
Penalty if found without a pass = $500
Probability of getting caught = 0.1
Expected value if you buy the day pass = -$20
Expected value if you don't buy the pass = - (fine) * (Probability of getting caught) = - (0.1 x 500) = -$50
Since EV if you do not buy the pass < EV if you buy the pass, the wise choice would be to buy the pass.