Figures obtained from a city\'s police department seem to indicate that of all m

Question

Figures obtained from a city's police department seem to indicate that of all motor vehicles reported as stolen, 67% were stolen by professionals (P), whereas 33% were stolen by amateurs (primarily for joy rides) (A). Of the vehicles presumed stolen by professionals, 29% were recovered within 48 hours (R<48), 21% were recovered after 48 hours (R>48), and 50% were never recovered (N). Of the vehicles presumed stolen by amateurs, 30% were recovered within 48 hours, 66% were recovered after 48 hours, and 4% were never recovered.

What is the probability that a vehicle stolen by a professional in this city will be recovered within 48 hours?

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

Explanation / Answer

Here, we are given that:

P( P) = 0.67, P( A) = 0.33

P( R < 48 | P) = 0.29 , P( R> 48 | P) = 0.21 and P( N | P) = 0.5

Also for amateurs, P( R < 48 | A) = 0.3, P( R > 48 | A) = 0.66 and P(N | A) = 0.04

Using law of total probability, we get:

P(R < 48 ) = P( R < 48 | P)P(P) + P( R < 48 | A) P(A) = 0.29*0.67 + 0.3*0.33 = 0.2933

Therefore 0.2933 is the required probability here.

again using the law of total probability we get:

P(N) = P( N | P)P(P) + P( N | A) P(A) = 0.5*0.67 + 0.04*0.33 = 0.3482

Therefore 0.3482 is the required probability here.

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