Answer to Question #291987 in Statistics and Probability for ali

Question

Suppose that the four inspectors at a film factory are supposed to stamp the expiration date on each package of film at the end of the assembly line. John, who stamps 20% of the packages, fails to stamp the expiration date once in every 200 packages; Tom, who stamps 60% of the packages, fails to stamp the expiration date once in every 100 packages; Jeff, who stamps 15% of the packages, fails to stamp the expiration date once in every 90 packages; and Pat, who stamps 5% of the packages, fails to stamp the expiration date once in every 200 packages. If a customer complains that her package of film does not show the expiration date, what is the probability that it was inspected by John?

Answer 1

Think through the following events:

 

A: the produce is not marked

 

B1: the produce is marked by John

 

B2: the produce is marked by Tom

 

 B3: the produce is marked y Jeff

 

B4: the produce is marked by Pat

 

Applying the rule of elimination, the formula would be:

 

P (A) = P (B1) P (A|B1) + P (B2) P (A|B2) + P (B3) P (A|B3) + P (B4) P (A|B4)

 

And the following are the probabilities:

 

P(B1)P(A|B1) = (.20)(1/200) = .001

 

P(B2)P(A|B2) = (.60)(1/100) = .006

 

P(B3)P(A|B3) = (.15)(1/90) = .00167

 

P(B4)P(A|B4) = (.05)(1/200) = .00025

 

The likelihood that the product is not imprinted is equal to .001 + .006 + .00167 + .00025 = .00892

 

The probability that it was reviewed by John is = .001/.00892 = .1121