Question

A company has 3 plants that produce a type of component. The first plant produces 30% with a defective rate of 1%. The second plant produces 20% with a defective rate of 2%. The third plant produces 50% with a defective rate of 3%. Suppose if we randomly take one component and find it is defective, what is the probability that this component is from the third plant?

Answer 1

Answer:0.681

Step-by-step explanation:

Given

Machine 1  produces 30 % component with defective rate of 1%

Machine 2 produces 20 % component with defective rate of 2%

Machine 3 produces 50 % component with defective rate of 3%

Probability that Component is defective

i.e. it can be from A , B or C

P(defective)$=0.3\times 0.01+0.2\times 0.02+0.5\times 0.03=0.022$

Probability it comes From third Plant i.e. From 3

$P(third\ Plant)=0.5\times 0.03=0.015$

Probability that Component is Defective and it comes from Third Plant

$P=\frac{0.015}{0.022}=0.681$