3 A manufacturer makes two models of an item model I which a

3. A manufacturer makes two models of an item: model I, which accounts for 80% of unit sales, and model II, which accounts for 20% of unit sales. Because of defects, the manufacturer has to replace (or exchange) 10% of its model I and 18% of its model II. If a model is selected at random, find the probability that it will be defective.

Solution

Let us draw probability tree for the given information

Products -- Model I -- 80% unit sales     

                                    -- 10% replace/excahgne

                 -- Model II -- 20% unit sales

                                   -- 18% replace/exchange

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A model is selected at random

It can be 1 or 2

Prob (random selection is defective) = P(model I and defective) + Prob (model II and defective)

= 0.5(0.1) + 0.5(0.18)

= 0.05+0.09

= 0.14