Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

A business has 3 departments. We will look at the wrong production of a particul

ID: 3273362 • Letter: A

Question

A business has 3 departments. We will look at the wrong production of a particular type of product that the company produces in all its departments. The three departments we can call A1, A2 and A3, and they account for 20, 70 and 10% of the production of this product as we see. Furthermore, it has been established that the error rate in A1 is 1%, the error in A2 is 0 , 5% and error rate in A3 is 0.1%.

a) Express the information of probabilities and find the likelihood that a random item of this type is flawless.

b) Find the likelihood that an error-produced product is from A2.

Explanation / Answer

a) Probability or the likelihood that a random item of this type would be flawless is computed as:

= 1- Probability that a random item of this type would be defective

= 1 - (0.2*0.01 + 0.7*0.005 + 0.1*0.001)

= 0.9944

Therefore 0.9944 is the required probability here.

b) Given that an error has occured, probability that is is from A2 is computed as:

= ( Probability that an error is produced and production was from A2 ) / Probability of an error

= 0.7*0.005 / (0.2*0.01 + 0.7*0.005 + 0.1*0.001)

= 0.0035/ ( 0.002 + 0.0035 + 0.0001)

= 0.625

Therefore 0.625 is the required probability here.