Drew L.
asked • 03/13/17defective item
defective item, 10 item, some are bad, probability without replacement
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1 Expert Answer
Erica H. answered • 03/13/17
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How many items are bad, and how many are you drawing? For what particular event are you trying to find the probability?
Drew L.
3 bad items, What is the probability that 1st part is goo, 2nd part is good, and no good parts?
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03/13/17
Erica H.
So I'm still not sure what the whole question is, but I'll help you out as much as I can.
If you have 10 pieces, and 3 of them are bad, there are 10-3=7 good pieces.
So, when you go to pull the first piece, there is a 7/10 chance that it will be good.
Without replacement means you don't put back that first good piece before trying to pull another one, so now you're pulling from a pool of 9 items, and if you pulled a good one before, then only 6 good ones are left.
So, when you go to pull the second piece, there is a 6/9 chance that it will be good.
You need both these events to occur, the first with a probability of 7/10 and the second with a probability of 6/9. To find the probability of BOTH of these events occurring, multiply the two probabilities. 7*6=42 and 10*9=90, so the new probability is 42/90 which can be reduced to 21/45 by dividing by 2/2 and then again to 7/15 by dividing by 3/3. 7 is a prime number, so that's as far as that can be reduced.
I can't tell from your question whether you need to include a third event in your probability, but the method will be the same if so.
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03/14/17
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03/13/17