Suppose that a product is produced in three factories X, Y and Z. It is known that factory X produces thrice as many items as factory Y, and that factories Y and Z produce the same number of items. Assume that it is known that 3 per cent of the itenis produced by each of the factories X and Z are defective while 5 per cent of those manufactured by factory Y are defective. All the items produced in the three factories are stocked, and an item of product is selected at random. (i) What is the probability that this item is defective? (ii) If an item selected at random is found to be defective, what is the probability that it was produced by factory X, Y and Z respectively?

Suppose that a product is produced in three factories X, Y and Z. It is known that factory X produces thrice as many items as factory Y, and that factories Y and Z produce the same number of items. Assume that it is known that 3 per cent of the itenis produced by each of the factories X and Z are defective while 5 per cent of those manufactured by factory Y are defective. All the items produced in the three factories are stocked, and an item of product is selected at random. (i) What is the probability that this item is defective? (ii) If an item selected at random is found to be defective, what is the probability that it was produced by factory X, Y and Z respectively?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Suppose that a product is produced in three
factories X, Y and Z. It is known that factory X
produces thrice as many items as factory Y,
and that factories Y and Z produce the same
number of items. Assume that it is known that
3 per cent of the itenis produced by each of the
factories X and Z are defective while 5 per cent
of those manufactured by factory Y are
defective. All the items produced in the three
factories are stocked, and an item of product is
selected at random.
(i) What is the probability that this item is
defective?
(ii) If an item selected at random is found to be
defective, what is the probability that it was
produced by factory X, Y and Z respectively?

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