Question

1. A company produces 1,000 refrigerators a week at three plants. Plant A produces 350 refrigerators a week, plant B produces 250 refrigerators a week, and plant C produces 400 refrigerators a week. Production records indicate that 5% of the refrigerators produced at plant A will be defective, 3% of those produced at plant B will be defective, and 7% of those produced at plant C will be defective. All the refrigerators are shipped to a central warehouse. If a refrigerator at the warehouse is found to be defective, what is the probability it was produced at plant A? Show your work if you would like full credit.

Answer 1

0.3302 or 33.02%

Explanation:

Expected defective from A = 0.05 x 350 = 17.5 defective refrigerators.

Expected defective from B = 0.03 x 250 = 7.5 defective refrigerators.

Expected defective from C = 0.07 x 400 = 28 defective refrigerators.

The probability of a refrigerator being produced at plant A, given that it is defective, is determined by dividing the expected number of defective refrigerators from plant A by the expected number of defective refrigerators from all plants:

`P = (17.5)/(17.5+7.5+28)\\ P=0.3302 = 33.02\%`

The probability it was produced at plant A is 0.3302 or 33.02%.