You decide to never put money in a 10cent parking meter You

You decide to never put money in a 10-cent parking meter. You base your decision on the assumption that there is a probability of 0.05 that you will be caught. The first offense costs nothing, the second costs 2 dollars, and subsequent offenses cost 5 dollars each. In these conditions, how does the expected cost of parking 100 times without paying the meter compare with the cost of paying the meter each time?

Solution

Probability of getting caught by not paying the meter=0.05

Expected no. of times of getting caught by not paying the meter 100 times=0.05*100=5

Expected cost=0+2+5+5+5=17 dollars

Expected cost when meter is paid each time=0.1*100=10 dollars.

Thus it is better to pay the meter if the probability of getting caught is 0.05. Since the cost of paying meter 100 times=$10 while the expected cost of paying fine for the offense is= $17.