Suppose that the four inspectors at a film factory are supposed to stamp the exp

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 package, fails to stamp the expiration date once in every 200 package. 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, sails to stamps the expiration date once every 90 packages; and Paul, 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 John inspected it?

Explanation / Answer

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 package, fails to stamp the expiration date once in every 200 package.
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, sails to stamps the expiration date once every 90 packages; and
Paul, 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 John inspected it?

probability that John stamps = 20% = 0.2
probability that Jonn fails to stamps = 1/200 = 0.005
probability that Tom stamps = 60% = 0.6
probability that Tom fails to stamps = 1/100 = 0.01
probability that Jeff stamps = 15% = 0.15
probability that Jeff fails to stamps = 1/90 = 0.0111111111111111
probability that Paul stamps = 5% = 0.05
probability that Paul fails to stamps = 1/200 = 0.005

probabiity that package doesnt show expiration date and john inspected it is =

P(John)*P(John fails to stmap) / (P(John)*P(John fails to stmap) + P(Tom)*P(Tom fails to stmap) + P(Jeff)*P(Jeff fails to stmap) + P(Paul)*P(Paul fails to stmap))

required probablity = (0.2*0.005)/(0.2*0.005 + 0.6*0.01 + 0.15*0.01111+ 0.05*0.005) = 0.1121 is ANSWER.

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