If on average 90% of meetings end in less than 2 hours, what is my best strategy?

Question

Every thursday i attend a business meeting which is scheduled to last 2 hours. I can either park in a public car park for standard fee of £1.20 or a parking meter for 50p for 2 hours. However the fine for parking at meter for more than 2 hours is £10. If on average 90% of meetings end in less than 2 hours, what is my best strategy?

Answer 1

Based on the information you have provided, you can calculate an expected cost of parking at the meter compared to the public car park, with the following assumptions:

1. When parking at a meter for more than two hours, you are certain to get a ticket.
2. Parking at the meter for more than 2 hours still only costs 50p (excluding the fine).
3. The 90% of meetings that end in under two hours allow enough time to reach your car (parked at the meter) before incurring a fine.

Now for the calculation:

Parking at the meter is expected to cost 0.5 pounds 90% of the time, and 0.5 pounds PLUS an additional 10 pounds 10% of the time. Therefore, the cost of parking at the meter (each Thursday) may be modeled as

(0.9)*(0.5) + (0.1)*(10.5) = 1.5 pounds

This comes out to more than the cost of parking in the garage, so from a statistical standpoint you can expect to save 30p each time by parking at the public car park.

EXTRA: What if you don't think that parking for more than 2 hours will always result in a fine?

We can include the probability of getting a fine given that you have parked for more than 2 hours in our calculation and determine the probability at which you would break even (meaning that parking at the car park or the meter would be expected to cost the same amount).

(0.9)(0.5) + (0.1)(10.5)(x) + (0.1)(0.5)(1-x) = 1.2

0.45 + 1.05x + 0.05 - 0.05x = 1.2

0.5 + 1.0x = 1.2

x = 0.7, where x is the probability of getting a ticket given that you have parked for over 2 hours at which you would break even.

In other words,

1. If you believe that the probability of getting a ticket is greater than 70%, then you should definitely park in the public car park.
2. If you believe that the probability of getting a ticket is less than 70%, then you should park at the meter (but realize that the savings might not be so significant if the actual probability is close to 70%).
3. If you believe that the probability of getting a ticket is exactly 70%, then it actually doesn't matter where you park. You will pay the same either way.

Of course, this probability is not constant and most likely grows as you remain parked at the meter for longer beyond the 2 hour limit.

In summary, park at the car park. Unless you have some knowledge regarding the probability of getting a ticket given that you overstay your welcome at the meter, this is your safest bet.