An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accidents are 0.01, 0.03 and 0.15 respectively.

One of the insured persons meets with an accident. What is the probability that he is a scooter driver?

Given: let E₁ be the event that the driver is a scooter driver, E₂ be the event that the driver is a car driver and E₃ be the event that the driver is a truck driver. Let A be the event that the person meet with an accident.

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

Then

And

And

As we a headed coin has head on both sides so it will shows head.

Also P(A|E₁) = P (accident of a scooter driver)

And P(A|E₂) = P (accident of a car driver)

And P(A|E₃) = P (accident of a truck driver)

Now the probability that the driver is a scooter driver, being given that he met with an accident, is P(E₁|A).

By using bayes’ theorem, we have: