A manufacturer makes two models of an item: model I, which accounts for 86% of unit sales, and model II, which accounts for 14% of unit sales. Because of defects, the manufacturer has to replace (or exchange) 10% of its model I and 17% of its model II. If a model is selected at random, find the probability that it will be defective. Please round the final answer to 2 or 3 decimal places.

Probability that it will be defective = 0.1098

Step-by-step explanation:

We are given that a manufacturer makes two models of an item: model 1 and model 2.

Let Probability of unit sales made through model 1, P(A) = 0.86

Probability of unit sales made through model 2, P(B) = 0.14

Let D = even that item is defective

Probability that items are defective given model 1 was used, P(D/A) = 0.10

Probability that items are defective given model 2 was used, P(D/B) = 0.17

So, If a model is selected at random, the probability that it will be defective is given by = P(A) * P(D/A) + P(B) * P(D/B)

                 = 0.86 * 0.10 + 0.14 * 0.17

                 = 0.086 + 0.0238 = 0.1098 .

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