Vehicles

[sportywarbz]

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 joy rides). Of those vehicles stolen by professionals, 21% were recovered within 48 hours, 15% were recovered after 48 hours, and 64% were never recovered. Of those vehicles presumed stolen by amateurs, 44% were recovered within 48 hours, 50% were recovered after 48 hours, and 6% were never recovered.
(a) Draw a tree diagram representing the data. (Do this on paper, your instructor may ask you to turn in this work.)

(b) What is the probability that a vehicle stolen by a professional in this city will be recovered within 48 hours? (Round your answer to two decimal places.)=.21

(c) What is the probability that a vehicle stolen in this city will never be recovered? (Round your answer to four decimal places.)

I need help with part c please.

 

[wjm11]

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 joy rides). Of those vehicles stolen by professionals, 21% were recovered within 48 hours, 15% were recovered after 48 hours, and 64% were never recovered. Of those vehicles presumed stolen by amateurs, 44% were recovered within 48 hours, 50% were recovered after 48 hours, and 6% were never recovered.
(a) Draw a tree diagram representing the data. (Do this on paper, your instructor may ask you to turn in this work.)

(b) What is the probability that a vehicle stolen by a professional in this city will be recovered within 48 hours? (Round your answer to two decimal places.)=.21

(c) What is the probability that a vehicle stolen in this city will never be recovered? (Round your answer to four decimal places.)

I need help with part c please.

Just draw your tree diagram and the rest is easy.

Start your tree diagram with two branches – one for professionals (.64) and one for joy-riders (.36). Off of each of these two branches, you’ll have three more branches – 24 hour, 48 hour, and never recovered. Place the appropriate probabilities on each branch.

Following the pros and never recovered branches, you have (.64)(.64) = .4096.
Following the joy-riders and never recovered, you have (.36)(.06) = .0216.
Just add them up.