ou’ve asked two interns to make you a reagent that you need to use in a water tr

Question

ou’ve asked two interns to make you a reagent

that you need to use in a water treatment process

At this point, you’ve improved your understanding of statistics, which you will

now use to impose your authority. The interns are cranking away at making

reagents: Intern 1 outputs 48 batches of the reagent a week, while Intern 2

makes 46 batches. If a reagent does not meet your standards you throw it

away. Through good book keeping, you’ve found that 2% of reagents made

by Intern 2 do not meet your standards, while about 9% of reagents made by

Intern 1 (of course) do not meet your standard. Define the following events

Ebad = batch doesnt meet standard

E1 = Batch made by intern 1

E2 = Batch made by intern 2

This week, unfortunately, none of the batches were labeled. You just have a

pile of reagents and do not know which intern made which batch.

(a) If you pull a reagent from the pile, find the probability that it will not meet

your standards.

(b) If the reagent you pulled is bad, find the probability that is was made by

Intern 1.

(c) If the reagent you pulled is bad, find the probability that is was made by

Intern 2.

Explanation / Answer

a)

probability that it will not meet your standards. =P(Ebad) =P(E1)*P(Ebad|E1)+P(E2)*P(Ebad|E2)

=(48/(48+46))*0.09+(46/(48+46))*0.02=0.0557

b)

probability that is was made by Intern 1; given bad =P(E1|bad) =P(E1)*P(Ebad|E1)/P(E1bad)

=(48/(48+46))*0.09/0.0557 =0.8244

c)probability that is was made by Intern 2; given bad =P(E2|bad) =P(E2)*P(Ebad|E2)/P(E1bad)

=(46/(48+46))*0.02/0.0557 =0.1756

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