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

Solution:

Let represent the driver being a scooter driver, represent the driver being a car driver, and represent the driver being a truck driver. Assume that the person is involved in an accident.

total number of drivers

Then

Because a headed coin has a head on both sides, it will display one.

Also accident of a scooter driver

And accident of a car driver

And accident of a truck driver

Because a headed coin has a head on both sides, it will display one. Given that the driver was involved in an accident, the probability that he was a scooter driver is .

We have used Bayes’ theorem to arrive at our conclusion.

We may now retrieve the result by swapping the values.