A distributor of outdoor yard lights has four suppliers. This past season she purchased 40% of the lights from Franklin Lighting, 30% from Wilson & Sons, 20% from Evergreen Supply, and the rest from A. L. Scott. In prior years, 3% of Franklin's lights were defective, 6% of the Wilson lights were defective, 2% of Evergreen's were defective, and 8% of the Scott lights were defective. When the lights arrive at the distributor, she puts them in inventory without identifying the supplier. Suppose that a defective light string has been pulled from inventory; what is the probability that it was supplied by Franklin Lighting?
A) 0.33
B) 0.45
C) 0.18
D) 0.29

Question

Quizplus · Accepted Answer

To find the probability that a defective light string was supplied by Franklin Lighting, we use Bayes' theorem. First, calculate the overall probability of a defective light string:- Franklin: 40% * 3% = 1.2%- Wilson & Sons: 30% * 6% = 1.8%- Evergreen: 20% * 2% = 0.4%- A. L. Scott: 10% (100% - 40% - 30% - 20%) * 8% = 0.8%Total probability of a defective light string = 1.2% + 1.8% + 0.4% + 0.8% = 4.2%Probability the defective light is from Franklin = (Probability of picking a Franklin light) * (Probability it is defective) / (Total probability of a defective light) = 1.2% / 4.2% = 0.2857 or 28.57%, which rounds to 0.29.

A Distributor of Outdoor Yard Lights Has Four Suppliers