Your assembly plant buys identical widgets from 3 suppliers, A, B, and C. Suppliers A and B each supplies a quarter of your widgets each day, whereas Supplier C supplies the remaining 50%. Of the widgets supplied by A, B, and C, the average numbers of defective widgets are 5%, 3%, and 7%, respectively. (a) If a widget is selected at random, what is the probability of it being defective? Let A, B, C be the event of a randomly picked widget being sourced by suppliers A, B, and C, respectively. Furthermore, let D be the event of a randomly-picked widget being defective. Use these symbols A, B, C, and D when you do this problem. (b) What is the probability of a randomly-picked widget being supplied by A and also being defective? (c) If a randomly-picked widget is defective, what’s the probability of it having been supplied by A? (d) If a randomly-picked widget is defective, what’s the probability of it having been supplied by B? By C? What's the sum of the 3 probabilities obtained in parts (c) and (d)? Is it as you'd expect?
Your assembly plant buys identical widgets from 3 suppliers, A, B, and C. Suppliers A and B each supplies a quarter of your widgets each day, whereas Supplier C supplies the remaining 50%. Of the widgets supplied by A, B, and C, the average numbers of defective widgets are 5%, 3%, and 7%, respectively.
(a) If a widget is selected at random, what is the
(b) What is the probability of a randomly-picked widget being supplied by A and also being defective?
(c) If a randomly-picked widget is defective, what’s the probability of it having been supplied by A?
(d) If a randomly-picked widget is defective, what’s the probability of it having been supplied by B? By C? What's the sum of the 3 probabilities obtained in parts (c) and (d)? Is it as you'd expect?
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