Question

The quality control department of the company has determined that 7% of the compact disks produced by manufacturer I are defective, 5% of those produced by manufacturer II are defective, and 4% of those produced by manufacturer III are defective. Manufacturers I, II, and III supply 37%, 45%, and 18%, respectively, of the compact disks used by the company. What is the probability that a randomly selected compact disk is defective?

Answer 1

To calculate the probability of selecting a defective compact disk from the company's supply, multiply the defect rate of each manufacturer by their proportion of supply and add the results. The combined probability is 5.49%.

Step-by-step explanation:

The probability that a randomly selected compact disk is defective can be calculated by using the law of total probability. This requires taking into account the defect rates and supply proportions for all manufacturers.

The probability that a randomly selected compact disk is defective is 0.0549 or 5.49%.

To find the overall probability of getting a defective disk, we multiply the probability of a disk being defective from each manufacturer by the proportion of disks they supply, and then sum these values:

• P(defective from I) = 0.37 * 0.07 = 0.0259
• P(defective from II) = 0.45 * 0.05 = 0.0225
• P(defective from III) = 0.18 * 0.04 = 0.0072

Adding these probabilities gives the total probability of a defective disk:

0.0259 + 0.0225 + 0.0072 = 0.0549 or 5.49%