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

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* 0.01+0.2* 0.02+0.5* 0.03=0.022`

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

`P(third\ Plant)=0.5* 0.03=0.015`

Probability that Component is Defective and it comes from Third Plant

`P=(0.015)/(0.022)=0.681`