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Statistics / Fundamentals of Probability, with Stochastic Processes 3 / Chapter 4.5 / Problem 2

Fundamentals of Probability, with Stochastic Processes | 3rd Edition | ISBN: 9780131453401 | Authors: Saeed Ghahramani

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In a certain part of downtown Baltimore parking lots

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QUESTION:

In a certain part of downtown Baltimore parking lots charge $7 per day. A car that is illegally parked on the street will be fined $25 if caught, and the chance of being caught is 60%. If money is the only concern of a commuter who must park in this location every day, should he park at a lot or park illegally?

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QUESTION:

In a certain part of downtown Baltimore parking lots charge $7 per day. A car that is illegally parked on the street will be fined $25 if caught, and the chance of being caught is 60%. If money is the only concern of a commuter who must park in this location every day, should he park at a lot or park illegally?

ANSWER:

Step 1 of 2

In a certain part of downtown Baltimore parking lots charge $7 per day. A car that is illegally parked on the street will be fined $25 if caught, and the chance of being caught is 60%.

Let be the random variable that denotes the total earning of the commuter.

Then, considers two values, either 7 or the fine charge -25. Here, the negative sign occurs due to the fine.

Now, the probability that the commuter gets caught is 60%. Therefore,

The probability that the commuter doesn’t get caught is 40%. Therefore,

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