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.
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