The following case study was reported in the article "Parking Tickets and Missing Women," which appeared in an early edition of the book Statistics: A Guide to the Unknown. In a Swedish trial on a charge of overtime parking, a police officer testified that he had noted the position of the two air valves on the tires of a parked car: To the closest hour, one was at the one o'clock position and the other was at the six o'clock position. After the allowable time for parking in that zone had passed, the policeman returned, noted that the valves were in the same position, and ticketed the car. The owner of the car claimed that he had left the parking place in time and had returned later. The valves just happened by chance to be in the same positions. An "expert" witness computed the probability of this occurring as (1/12)(1/12) = 1/144.
a. What reasoning did the expert use to arrive at the probability of 1/144?
b. Can you spot the error in the reasoning that leads to the stated probability of 1/144?
c. What effect does this error have on the probability of occurrence?
d. Do you think that 1/144 is larger or smaller than the correct probability of occurrence?