Answer:
The probability that it came from plant 2 is 0.224.
Explanation:
We are given that Quality Motors has three plants. Plant 1 produces 35% of the car output, plant 2 produces 20% and plant 3 produces the remaining 45%.
One percent of the output of plant 1 is defective, 1.8% of the output of plant 2 is defective and 2% of the output of plant 3 is defective.
Let the Probability that car output is produced by Plant 1 = P(A) = 0.35
Probability that car output is produced by Plant 2 = P(A) = 0.20
Probability that car output is produced by Plant 3 = P(A) = 0.45
Also, let D = event that output is defective
So, Probability that output defective given that it was produced by plant 1 = P(D/A) = 0.01
Probability that output defective given that it was produced by plant 2 = P(D/B) = 0.018
Probability that output defective given that it was produced by plant 3 = P(D/C) = 0.02
Now, a car is chosen at random from the annual output and is found defection so, the probability that it came from plant 2 is = P(B/D)
We will use the concept of Bayes' Theorem here to calculate the above probability.
SO, P(B/D) =
=
=
= 0.224
Hence, the required probability is 0.224.