Chapter 7.6, Problem 22E

CAR THEFT Figures obtained from a city’s police department indicate that of all the 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 professional, $24\%$ were recovered within $48\text{hours}$, $16\%$ were recovered after $48\text{hours}$, and $60\%$ were never recovered. Of the vehicles presumed stolen by amateurs, $38\%$ were recovered within $48\text{hours}$, $58\%$ were recovered after $48\text{hours}$, and $4\%$ were never recovered. If a stolen vehicle was recovered after $48\text{hours}$, what is the probability that it was stolen by professional?