# One of The Insured Persons Meets With an Accident :

An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 trucks drivers. The probabilities of an accident involving a scooter driver, car driver and a truck driver are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. The probability that the person is a scooter driver is

- 1/52
- 3/52
- 15/52
- 19/52

**Answer: (1) 1/52**

**Explanation: –
**Let event that the drive is a scooter driver = A,

the event that the drive is a car driver = B

And event that the drive is a truck driver = C

The total number of drivers = 2000 + 4000 + 6000 = 12000

Then, P (A) = 2000/12000 = 1/6

Therefore, P (B) = 4000/12000 = 1/3

Therefore, P (C) = 6000/12000 = ½

Let the event that the person meets with an incident = D

Then, P (D/A) = 0.01 = 1/100

P (D/B) = 0.03 = 3/100

P (D/C) = 0.15 = 15/100

By Babe’s theorem,

P (A/D) = (P (A) . P (D/A)/P (A) . P (D/A) + P(B). P (D/B) + P (C). P (D/C)

P (A/D) = (1 x 1/6 x 100)(1 x 1/6 x 100 + 1 x 3/(3 x 100 + 1 x 15/2 x 100)

= (1/6) / (1/6 + 3/3 + (15/2)

= (1/6)/(104/12)

= 1/52

Hence, the answer is (1) 1/52.