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An insurance company insured 2000 scooters and 3000 motorcycles. The probability of an accident involving a scooter is 0.01 and that of a motorcycle is 0.02. An insured vehicle met with an accident. Find the probability that the accidented vehicle was a motorcycle.

Answer»


SOLUTION :LET `E_1 and E_2` be the events that an insred vehicle is a SCOOTER and a motorcycle respectively.
Let E be the eventthat the INSURED vehicle meets and ACCIDENT.
`P(E_1)=2000/((2000+3000))=2/5,P(E_2)=3000/5000=3/5`,
`P(E//E_1)=0.01 and P(E//E_2)=0.02`
`:. P(E_2//E)=(P(E_2).P(E//E_2))/(P(E_1).P(E//E_1)+P(E_2).P(E//E_2))`
`=((3/5xx0.02))/((2/5xx0.01)+(3/5xx0.02))=3/4`.


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