An automobile insurance company classifies drivers into 3 classes: class A (good risks), class B (medium risks), and class C (poor risks). The percentage of drivers in each class is: class A, 20%; class B, 65%; and class C, 15%. The probabilities that a driver in one of these classes will have an accident within one year are given by 0.01, 0.02, and 0.03, respectively. After purchasing an insurance policy, a driver has an accident within the first year. What is the probability that the driver is a class A risk? A class B risk? A class C risk?

Question

An automobile insurance company classifies drivers into 3 classes: class A (good risks), class B (medium risks), and class C (poor risks).  The percentage of drivers in each class is: class A, 20%; class B, 65%; and class C, 15%.  The probabilities that a driver in one of these classes will have an accident within one year are given by 0.01, 0.02, and 0.03, respectively.  After purchasing an insurance policy, a driver has an accident within the first year.  What is the probability that the driver is a class A risk?  A class B risk?  A class C risk?

anonymous · Answer

Im having trouble setting up the equation.

is the 0.01,0.02,0.03 refering to a conditional probability or a intersection? (E.g class A given an accident, or Class A and accident?)

Also, I always seem to end up needing to have P(accident)...am I setting it up wrong?

kropot72 · Answer

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The above probability tree shows how to calculate the required probabilities. In this question each required probability is an intersection.