In downtown of a citiy, there is a very busy parking space. Cars stay at this sp

Question

In downtown of a citiy, there is a very busy parking space. Cars stay at this space for time that is uniform between 0 and 4 hours. Whenever a car leaves, another car takes its place immediately. Parking in this space is legally limited to 2 hours. To enforce this, parking officials pass by every 2 hours. Every time they pass they mark the currently parked car with a chalk. If the marked car is still there when they pass 2 hours later, it gets a ticket. What is the probability the parking officials will assign a ticket in a given visit?

Explanation / Answer

Let T denote the parking time of a particular car. Then, T ~ Uniform (0,4).

In the long run,

Probability that the parking officials will assign a ticket in a given visit = P(T > 2) = (4-2)/(4-0) = 0.5 Answer

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