Question

An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probabilities of an accident are 0.01, 0.03 and 015 respectively. One of the insured person meets with an accident. What is the probability that he is a scooter driver ?

Answer 1

Let 

E₁ : Event that scooter driver is insured 

E₂ = Event that car driver is insured 

E₃ = Event that truck driver is insured and 

A : Even that an accident occurs. 

A company insured 2000 scotter drivers, 4000 car drivers and 6000 truck drivers. 

∴ Total number of drivers insured = 2000 + 4000 + 6000 = 12000 

∴ Probability of scooter drivers insured

P(E₁) = 2000/12000 = 1/6

Probability of car drivers insured

P(E₂) = 4000/12000 = 1/3

Probability of truck drivers insured

P(E₃) = 6000/12000 = 1/2

Probability of scooter drivers accidents

= P(A/E₁) = 0.01

Probability of car drivers accidents

P(A/E₂) = 0.03

Probability of truck drivers accidents

P(A/E₃) = 0.15

A person meets an accident who is insured. 

∴ Probability that the persons is a scooter driver

Hence, required probability : 1/52