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 ______ 

विकल्प

• `10/71`

• `16/71`

• `40/71`

• `21/71`

Answer 1

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`