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The ABC Beads Company sells packages marked “5,000 beads.” In a recent quality-control experiment, the plant managers collected data on their two packing machines to see if they overcount or undercount the number of beads in a package. The table below summarizes the data.

A customer decides to count the beads in a package that she purchases from ABC Beads. She finds that it has more than the advertised 5,000 beads. What is the probability that this package came from Machine 2?

The ABC Beads Company sells packages marked 5000 beads In a recent qualitycontrol experiment the plant managers collected data on their two packing machines to class=

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Answer:
The probability that the package came from Machine 2 given that it contains more than 5,000 beads is 0.3333.

Explanation:
Using Bayes' theorem:
P(M2|More) = (P(More|M2) * P(M2)) / P(More)

P(More) = (P(More|M2) * P(M2)) + (P(More|~M2) * P(~M2))

Calculate P(More), then use Bayes' theorem to find P(M2|More).

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