SOLUTION: Machines A, B,C of a ballpoint pen manufacturing industry produces 20%,30% and 50% of total output, while 5%,3% and 4% of the products are defective in order. From a day's product

Question 1094776: Machines A, B,C of a ballpoint pen manufacturing industry produces 20%,30% and 50% of total output, while 5%,3% and 4% of the products are defective in order. From a day's product a pen is taken at random and found defective. What is the probability that it was from machines A & C??
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Any pen selected is from machine A or machine B or machine C; it can't be "from machines A & C", as your question asks. So I don't know what you are really asking.

Of each 1000 pens manufactured, 200 are from A, 300 from B, and 500 from C. The defective pens are
5% of the 200 produced by A (10);
3% of the 300 produced by B (9); and
4% of the 500 produced by C (20)

There are a total of 39 defective pens. If a defective pen is found, the probability is
10/39 that it was from A;
9/39 (=3/13) that it was from B; and
20/39 that it was from C.

And to answer the question you actually asked, the probability is 0 that it came from A and C.
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