SOLUTION: hello please help me with this question: three different machines M1,M2,and m3 were used for producing a large batch of similar manufactured items. suppose that 20% of the items we

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Question 909156: hello please help me with this question: three different machines M1,M2,and m3 were used for producing a large batch of similar manufactured items. suppose that 20% of the items were produced by m1,30% by m2 and 50% by m3.suppose further that 1% of the items produced by m1 are defective,that2% of the items produced by m2 are defective and that 3% of the items produced by m3 are defective.
i) suppose one item is selected at random from the entire batch and it is found to be defective.determine the probability that this item was produced by m2
ii) suppose one item is selected at random from the entire batch and it is found to be nondefective. Determine the probability that it was produced by m2.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
hello please help me with this question: three different machines M1,M2,and m3 were used for producing a large batch of similar manufactured items. suppose that 20% of the items were produced by m1,30% by m2 and 50% by m3.suppose further that 1% of the items produced by m1 are defective,that2% of the items produced by m2 are defective and that 3% of the items produced by m3 are defective.
The easiest way to understand it and to do it is to pretend that exactly 
1000 items were produced, 200 by m1, 300 by m2, and 500 by m3. 1% of 200 is 2,
2% of 300 is 6, and 3% of 500 is 15. 

         200 items produced by m1,  2 bad and 198 good.
         300 items produced by m2,  6 bad and 294 good.
         500 items produced by m3, 15 bad and 485 good.
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Totals: 1000 items produced,       23 bad and 977 good.

i) suppose one item is selected at random from the entire batch and it is found to be defective.determine the probability that this item was produced by m2
That's 6 out of 23 or 6/23 or approximately 26.1%.

ii) suppose one item is selected at random from the entire batch and it is found to be nondefective. Determine the probability that it was produced by m2.
That's 294 out of 977 or 294/977 or approximately 30.1%.

Edwin