Economics+395+PS1+Fall+2008 - Economics 395 Topics in Risk...

Economics 395
Topics in Risk and Uncertainty
Homework Problem Set 1
Problem One
This problem is also presented in the following article, available on the CTools site:
Salop S., “Evaluating Uncertain Evidence with Sir Thomas Bayes: A Note for
Teachers, ” The Journal of Economic Perspectives Vol 1 No 1, pp 155-159.
In the town of Springfield, there are two taxi cab companies: Blue Taxi and Green Taxi.
All Blue Taxis are blue, and all Green Taxis are green. Blue Taxi is a larger company:
80% of all taxis in Springfield are Blue Taxis.
One night, a pedestrian is hit by a car and is killed. The single witness to the incident
insists that the car she saw hit the pedestrian was clearly a taxi, and was colored green.
She concludes that it must have been a Green Taxi. She estimated that the taxi was
traveling at around 30 mph, and viewed it under normal street lights from a distance of
about 30 yards. The family of the deceased pedestrian brings a wrongful death suit
against the Green Taxi Company, and the eye-witness testifies.
The attorney for the defendant produces evidence that eye-witnesses can make mistakes.
His studies show that a green colored car is identified as green only around 3/4 of the
time, and a blue colored car is identified as blue only around 2/3 of the time (when testing
takes place under normal street lights, at night, from a distance of 30 yards).
Use an event tree to determine the probability that the car the witness saw and identified
as green was indeed green. If this case is to be decided “on the balance of probabilities”,
do you think that Green Taxi should be held liable for the death of the pedestrian?
Problem Two
In 1988, O J Simpson entered a plea of “no contest” to a charge of assaulting his wife,
Nicole Brown Simpson. During Simpson’s subsequent trial for the murder of his wife,
the prosecution tried to introduce this prior conviction as evidence of Simpson’s guilt.