SOLUTION: A motor company produces their cars in two plants. Plant A produced 80% of all 2014 cars. 25% of all cars produced in Plant A had at least one major defect. Plant B produced the

Algebra ->  Probability-and-statistics -> SOLUTION: A motor company produces their cars in two plants. Plant A produced 80% of all 2014 cars. 25% of all cars produced in Plant A had at least one major defect. Plant B produced the      Log On


   

Question 928120: A motor company produces their cars in two plants. Plant A produced 80% of all 2014 cars. 25% of all cars produced in Plant A had at least one major defect. Plant B produced the remaining 20%. 8% of all cars produced at Plant B had at least one major defect. A 2014 Car is selected at random.
a) what is the probability that it had a major defect?
b) If a 2014 motor car is defective what is the probability that it was produced in Plant A?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Plant A: 80%(25% with at least one major defect)
Plant B: 20%(8% with at least one major defect)
Car selected at random
P(had a defect) = .80(.25) + .20(.08)= .216 0r 21.06%
......
P(A|B) = P(A and B)/P(B)
P(Plant A |def ) = .80(.25)/.216 = .2/.216 = .9259 0r 92.59%