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Probability Dependent Events

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Joined: 17 Jul 2011
Posts: 8
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Kudos [?]: 1 [0], given: 4

Probability Dependent Events [#permalink] New post 23 Jun 2012, 03:48
Hi,

Need help to know the correct solution.

1 In a shipment of 20 computers, 3 are defective. Three computers are randomly selected and tested. What is the probability that all three are defective if the first and second ones are replaced after being tested?


Probability

3 X 3 X 3 = 27
20 20 20 8000


2 In a shipment of 20 computers, 3 are defective. Three computers are randomly selected and tested. What is the probability that all three are defective if the first and second ones are not replaced after being tested?


Probability

3 X 2 X 1 = 6
20 19 18 6840

Probability

3 In a shipment of 20 computers, 3 are defective. Three computers are randomly selected and tested. What is the probability that all three are NOT defective if the first and second ones are not replaced after being tested?

Probability

1 X 1 X 1 = 1
17 16 15 4080


4 In a shipment of 20 computers, 3 are defective. Three computers are randomly selected and tested. What is the probability that all three are NOT defective if the first and second ones are replaced after being tested?

Probability

1 X 1 X 1 = 1
17 17 17 4913



Regards
Sanjiv
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Re: Probability Dependent Events [#permalink] New post 04 Jul 2012, 08:54
Hi Sanjiv,

It seems to me that numbers 1 & 2 are right on the money, but 3 & 4 are a little off.

You correctly setup numbers 1 & 2 with the probability of event 1 times the probability of event 2 etc. Question3 wants to know the probability of NOT picking defective computers. In the first pick there is a 17/20 chance of not picking a defective computer. In the second pick there is a 16/19 chance, and in the third pick there is a 15/18 chance, which equals 17/20 times 16/19 times 15/18. In question three it would be (17/20) (17/20) (17/20), or (17/20)^3.

From questions 1 and 2 it seems that you have a good grasp of how to do this type of question and that you just made a careless error on questions 3 and 4.

Finally, I don`t think that this is a dependent probability question. Each pick is totally independent of the other picks (although the probability has to be adjusted for how many objects are left). A dependent probability is when one event has some influence over another event occurring; for example, in pitching, where a pitcher is more likely to pitch a strike after having pitched a strike, in which case when calculating the chance of a strike we have to adjust for the probability of the previous pitch being a strike. To the best of my recollection I have never come across a dependent probability question on any GMAT prep test or on the GMAT itself.

Anyways, I hope this helps and best of luck to you,
David
Re: Probability Dependent Events   [#permalink] 04 Jul 2012, 08:54
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