Chapter 7.5, Problem 42E

CAR THEFT Figures obtained from a city's police department seem to indicate that of all motor vehicles reported as stolen, $64\%$ were stolen by professionals, whereas $36\%$ were stolen by amateurs (primarily for joyrides). Of the vehicles presumed stolen by professionals, $24\%$ were recovered within $48\text{hr}$, $16\%$ were recovered after $48\text{hr}$, and $60\%$ were never recovered. Of the vehicles presumed stolen by amateurs, $38\%$ were recovered within 48 hr, $58\%$ were recovered after $48\text{hr}$, and $4\%$ were never recovered.

a. Draw a tree diagram representing these data.

b. What is the probability that a vehicle stolen by a professional in this city will be recovered within $48\text{hr}$?

c. What is the probability that a vehicle stolen in this city will never be recovered?