You Choose To Park Your Car In A Metered Parking Spot Where The Cost Of Parking For 1 Hour Is $1.50. The Cost Of A Parking Ticket Is $15. Historically, The Local Police Only Catch One Out Of Every 12 Parking Violators In A Given Hour. You Are Trying To Determine If It’s
What is the idea behind the question..?
Topic Parking probabilities and expected value calculations.
What is this question about..? This question presents a scenario where you have parked your car in a metered parking spot, and you need to weigh the cost of paying for parking versus risking a parking ticket. The question introduces the probability of getting caught by the local police, adding a layer of decision-making complexity to the problem.
The Correct Answer and Explanation is :
The question is about calculating the expected value of parking in a metered spot where you risk receiving a parking ticket, considering both the cost of paying for parking and the chance of getting caught. This is a typical problem in probability and expected value calculations, which are used to make decisions based on both risks and rewards.
Step-by-Step Breakdown
The given information includes:
- Parking cost: $1.50 per hour.
- Ticket cost: $15.00 if caught.
- Probability of getting caught: 1 in 12, or approximately 0.0833 (1/12).
- Probability of not getting caught: 11 in 12, or approximately 0.9167 (11/12).
Calculate Expected Value (EV)
The expected value is a weighted average of all possible outcomes, taking into account both the costs and probabilities. The formula is:
[
EV = (P(\text{Caught}) \times \text{Cost of Ticket}) + (P(\text{Not Caught}) \times \text{Cost of Parking})
]
Using the given numbers:
[
EV = (0.0833 \times 15) + (0.9167 \times 1.50)
]
First, calculate the two components:
- ( 0.0833 \times 15 = 1.25 )
- ( 0.9167 \times 1.50 = 1.375 )
Now, add them together:
[
EV = 1.25 + 1.375 = 2.625
]
Interpretation of the Expected Value
The expected value of parking for an hour in this scenario is $2.625. This means, on average, you would spend $2.625 when considering the possibility of receiving a parking ticket.
- If you pay the meter, your cost is $1.50.
- If you risk a ticket, the expected cost, factoring in the probability of being caught, is $2.625.
Decision-Making
Based on this expected value calculation, you can decide whether it’s worth the risk of not paying the meter and possibly receiving a ticket. Since the expected cost of taking the risk ($2.625) is higher than simply paying the $1.50, it’s more economical to pay for the meter rather than risk a ticket.
In conclusion, the expected value calculation helps in making informed decisions by considering both the costs and probabilities involved in uncertain situations.