Real World Graduation, Question 90: Traffic Tickets

RealWorldGraduation_Question_90_Traffic_Tickets    <– PDF

A certain district lies along 25 miles of Highway U. S. 193, where the speed limit is 55 MPH throughout.  The police force in this district only issues speeding tickets based on radar readings, and the department regularly calibrates its equipment to make sure the readings are accurate.  It is also department policy to issue tickets only if the driver is more than 7 MPH over the speed limit (i.e., is considered speeding only if going more than 62 MPH).  Over the long run, the probability of getting a speeding ticket in this locality is 0.2 (meaning that over a long period of observations, 20% of people who are going faster than 62 MPH get tickets).

Consider the following situation. It is a Tuesday morning, after the rush hour.  The weather is clear and traffic is light in this locality on Hwy U. S. 193.  The police officers on duty at this time checking for speeders are 30% black male, 40% white male, 20% black female, and 10% white female, which is approximately the racial makeup of the force at most times.  A black woman in a foreign sports car was going 73 MPH in the 55 MPH zone.  What is the likelihood that she will get a speeding ticket?

a) 50%, because half the officers on duty are white

b) 100%, because she is driving a foreign car

c) Greater than 50%, because more than half the officers on duty are men

d) Either zero or 100%, depending on the race of the officer who sees her first

e) This question is illogical because everyone knows that black women never exceed the speed limit

(The answer is on p. 2 of the PDF.)


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