Question

A manufacturer makes two models of an item model 1 accounts for 80% of unit sales and model 2 accounts for 20% of unit sales because of defects the manufacturer has to replace 10% of model 1 and 18% of model 2 if a model is selected at random find the probability that it will be defective. Answer the following problems using multiplication rule make sure to reduce your fraction.

Answer 1

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) = 0.8 = 80/100

Probability of unit sales made through model 2, P(B) = 0.2 =20/100

Let D = event that item is defective

Probability that items are defective if given model 1 was used, P(D/A) = 0.10 10/100

Probability that items are defective if given model 2 was used, P(D/B) = 0.18 =18/100

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)

=80/100 * 10/100 + 20/100 * 18/100 = 4/5 * 1/10 + 1/5 * 9/50 = 29/250 = 0.116