question archive A public interest group was planning to make a court challenge to auto insurance rates in one of three cities: A (Atlanta), B (Baltimore), or C (Cleveland)
A public interest group was planning to make a court challenge to auto insurance rates in one of three cities: A (Atlanta), B (Baltimore), or C (Cleveland)
Subject:StatisticsPrice:2.87 Bought7
A public interest group was planning to make a court challenge to auto insurance rates in one of three cities: A (Atlanta), B (Baltimore), or C (Cleveland). The probability that it would choose Atlanta was 0.40; Baltimore was 0.35; Cleveland was 0.25. The group also knew that it had a 45 percent chance of favorable ruling if it chose Atlanta, 60 percent chance if it chose Baltimore, and 30 percent chance if it chose Cleveland.
a) Given the group did receive a favorable ruling, which city did it most likely to choose? Show your work.
b) What is the probability of a favorable ruling?
Purchase A New Answer
Custom new solution created by our subject matter experts
GET A QUOTE
Answer Preview
Answer:
P(A) = 0.4
P(B) = 0.35
P(C) = 0.25
P(F|A) = 0.45
P(F|B) = 0.60
P(F|C) = 0.30
a) P(A|F) = P(F|A)P(A)/[P(F|A)P(A) + P(F|B)P(B) + P(F|C)P(C)]
= (0.45)(0.40)/[(0.45)(0.40) + (0.60)(0.35) + (0.30)(0.25)]
= 0.3871
P(B|F) = P(F|B)P(B)/[P(F|A)P(A) + P(F|B)P(B) + P(F|C)P(C)]
= (0.60)(0.35)/[(0.45)(0.40) + (0.60)(0.35) + (0.30)(0.25)]
=0.4516
P(C|F) = P(F|C)P(C)/[P(F|A)P(A) + P(F|B)P(B) + P(F|C)P(C)]
= (0.30)(0.25)/[(0.45)(0.40) + (0.60)(0.35) + (0.30)(0.25)]
=0.1613
Most likely: Baltimore.
b) P(F) = P(F|A)P(A) + P(F|B)P(B) + P(F|C)P(C)
= (0.45)(0.40) + (0.60)(0.35) + (0.30)(0.25)
= 0.465
