An insurance company insures red and green cars. An actuary compiles the following data: Color of car Red Green Number insured 300 700 Probability an accident occurs 0.10 0.05 Probability that the claim exceeds the deductible, given an accident occurs from this group 0.90 0.80 The actuary randomly picks a claim from all claims that exceed the deductible. Calculate the probability that the claim is on a red car.

Answer: 2.7%Step-by-step explanation:Since the probability of having and accident or exceed the deductible does not depend on the color of the car, the events are independent. Recall that if two events A and B with probabilities P(A), P(B) of occurrence are independent, then P(A ∩ B) = P(A)P(B) There is a 300/1000 = 0.3 probability of choosing a random car. So, if the actuary randomly picks a claim from all claims that exceed the deductible,the probability that the claim is on a red car is 0.3*0.10*0.9 = 0.027 or 2.7%