Question

An insurance company insured 2000 scooter drivers, 4000 car drivers & 6000 truck drivers. The probabilities of their accident are 0.1, 0.3, and 0.2 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?

Answer 1

Number of scooter driver, S = 2000

Number of car drivers, C = 4000

Number of truck drivers, T = 6000

P(S) = 0.1

P(C) = 0.3

P(T) = 0.2

P(an accident with a scooter driver) $= \frac{S \times P(S)}{S \times P(S) + C \times P(C) + T \times P(T)}$

$= \frac{2000 \times 0.1}{2000 \times 0.1 + 4000 \times 0.3 + 6000 \times 0.2} \\ = \frac{200}{200+1200 + 1200} \\ = \frac{200}{2600} \\ = 0.0769$