Question

6.

A store sells widgets and is supplied by three major subcontractors. Subcontractor A is the more reliable company and only 2% of their widgets are defective. As such, company A makes 50% of the store’s supply. Subcontractor B makes 30% of the widgets and has a defection rate of 5%. Finally, subcontractor C makes the remaining 20% of the widget supply and 6% of those produced are defective.

A widget is examined at random and is found to be defective. For each subcontractor determine the probability that they manufactured this widget. Which subcontractor was most likely the maker of the defective item? Be sure to use a probability tree to answer this question, and to mention any theorems or results you use.

Answer 1