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Question
A company produces 10,000 items per day. On a particular day, 2500 items were produced on machine A, 3500 on machine B, and 4000 on machine C. The probability that an item is produced by the machines. A, B, C to be defective is respectively 2%, 3%, and 5%. If one item is selected at random from the output and is found to be defective, then the probability that it was produced by machine C, is ______
Options
`10/71`
`16/71`
`40/71`
`21/71`
Solution
A company produces 10,000 items per day. On a particular day, 2500 items were produced on machine A, 3500 on machine B, and 4000 on machine C. The probability that an item is produced by the machines. A, B, C to be defective is respectively 2%, 3%, and 5%. If one item is selected at random from the output and is found to be defective, then the probability that it was produced by machine C, is `underline(40/71)`.
Explanation:
Total number of defective items
= `2/100 xx 2500 + 3/100 xx 3500 + 5/100 xx 4000`
= 355
Number of defective items from machine C
= `5/100 xx 4000`
= 200
∴ Required probability = `200/355 = 40/71`
