5. Drivers in a certain population are classified as belonging to Class A, Class

Question

5. Drivers in a certain population are classified as belonging to Class A, Class B or Class C. 20% of the population belong to Class A, 60% belong to Class B and the rest to Class C. The probability that a driver of Class A will have an accident this year is 0.2. The probability that a driver of Class B will have an accident this year is.1 and the probability that a driver of Class C will have an accident this year is .05. If a driver has an accident this year, calculate the probability that that driver is of Class A

Explanation / Answer

P(driver has accident) =P(from class A and has accident+from class B and has accident+from class C and has accident)=0.2*0.2+0.6*0.1+0.2*0.05=0.11

therefore probability that driver is of class A given has an accident

=P(from class A and has accident)/P(has accident) =0.2*0.2/0.11=0.363636

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