Question

An insurance company issued 3000 scooters, 4000 cars, and 5000 trucks. The probability of the accident involving a scooter, a car and a truck are 0.02, 0.03 and 0.04 respectively. One of the insured vehicles meet with an accident. Then the probability that the scooter is

Answer 1

please find the attachment

Answer 2

No. Of scooter issued = 3000

No. Of cars issued= 4000

No. Of trucks issued= 5000

​Let E1, E2, E3 be the events of the insured vehicle i.e., scooter, car and truck respectively.

​P(E1) = 3000/(3000+4000+5000)

= 3000/12000

= 3/12

​P(E2) = 4000/(3000+4000+5000)

= 4000/12000

= 4/12

​P(E3) = 5000/(3000+4000+5000)

= 5000/12000

= 5/12

Let A be the event that a vehicle meets with an accident .

P(A/E1) = scooter is in a accident = 0.02

P(A/E2)= car is in a accident = 0.03

P(A/E3) = truck is in a accident= 0.04

Using Baye's rule to find the probability that the given vehicle is a scooter ,

P(E1)P(A/E1)/ (P(A/E1) P(E1) + P(A/E2) P(E2) + P(A/E3) P(E3))

=> ( 3/12 × 0.02 )/ ( 3/12×0.02 + 4/12×0.03 + 5/12×0.04 )

=> 3/19