Chapter 7.5, Problem 88E

Auto Theft Exercises 85–90 are based on the following table, which shows the probability that an owner of the given model would report his or her vehicle stolen in a 1-year period:⁶⁶

Model	Jeep Wrangler	Suzuki Sidekick (two-door)	Toyota Land Cruiser	Geo Tracker (two-door)	Acura Integra (two-door)
Probability	.0170	.0154	.0143	.0142	.0123
Model	Mitsubishi Montero	Acura Integra (four-door)	BMW 3-series (two-door)	Lexus GS300	Honda Accord (two-door)
Probability	.0108	.0103	.0077	.0074	.0070

In an experiment in which a vehicle is selected, consider the following events:

R: The vehicle was reported stolen.

J: The vehicle was a Jeep Wrangler

A2: The vehicle was an Acura Integra (two-door).

A4: The vehicle was an Acura Integra (four-door).

A: The vehicle was an Acura Integra (either two-door or four-door).

Which of the following is true?

(A) $P\left(R|A\right)=.0123+.0103=.0226$

(B) $P\left(R^{\prime }|A2\right)=1-.0123=.9877$

(C) $P\left(A2|A\right)=.0123/\left(.0123+.0103\right)\approx .544$

(D) $P\left(A|A{2}^{\prime }\right)=1-.0123=.9877$