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# A box contain 20 machine parts, 5 of them standard. A worker

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A box contain 20 machine parts, 5 of them standard. A worker [#permalink]

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10 Jun 2004, 18:08
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A box contain 20 machine parts, 5 of them standard. A worker takes out 3 parts at random. Find the probababilty that at least 1 out of three turns out to be standard.

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10 Jun 2004, 18:19
all possible ways = 20C3
number of ways to pick all three non-standard = 15C3

P = 1 - (15C3/20C3) = 15*14*13/20*19*18 = 0.6
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10 Jun 2004, 20:04
I concur with the reasoning but answer should be 1 - 91/228 = 137/228
Oh well, that was a very close approximation.
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Paul

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11 Jun 2004, 05:50
Avtar wrote:
A box contain 20 machine parts, 5 of them standard. A worker takes out 3 parts at random. Find the probababilty that at least 1 out of three turns out to be standard.

Atleast one will drive three cases :

Total : 20C3 = 1140
One standard and another 2 non-standard : 5C1 * 15C2 = 525
Two standard and another 1 non-standard : 5C2 * 15C1= 150
All three standard : 5C3 = 10

So answer should be: 685 / 1140 = 137 / 228

Dharmin

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11 Jun 2004, 06:23
Avtar wrote:
A box contain 20 machine parts, 5 of them standard. A worker takes out 3 parts at random. Find the probababilty that at least 1 out of three turns out to be standard.

P{1<=x<=3}=1-P{x=0} = 1-(15C3/20C3)= 1 - (15!*3!*17!)/(12!*3!*20!) = 1- 15*14*13/(20*19*18) = 1-91/228 = 137/228
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12 Jun 2004, 01:54
Avtar wrote:
A box contain 20 machine parts, 5 of them standard. A worker takes out 3 parts at random. Find the probababilty that at least 1 out of three turns out to be standard.

P(at least 1 is standard) = 1 - P(all are non-standard) = 1 - C[3,15]/C[3,20] = ...

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17 Jun 2004, 09:41
I got the process down, but keep forgetting to do
1- probability of getting an unfavorable outcome

and you know that the ETS will conveniently place the other answer among the choices

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17 Jun 2004, 09:43
lastochka wrote:
I got the process down, but keep forgetting to do
1- probability of getting an unfavorable outcome

and you know that the ETS will conveniently place the other answer among the choices

Yes, you should be aware of such traps in GMAT...

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17 Jun 2004, 09:43
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# A box contain 20 machine parts, 5 of them standard. A worker

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