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A shipment consists of 1,800 parts, some of which are defect

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Carcass
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A shipment consists of 1,800 parts, some of which are defect [#permalink] New post   24 Jul 2020, 10:54
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A shipment consists of 1,800 parts, some of which are defective. If a part is chosen from the shipment at random, the probability of it being defective is 1/9 the probability that it is not defective. How many of the parts in the shipment are defective?
(A) 90
(B) 120
(C) 180
(D) 200
(E) 900

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C
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Re: A shipment consists of 1,800 parts, some of which are defect [#permalink] New post   24 Jul 2020, 22:27
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Let number of defective shipments be x
=> Non defective = Total - defective = 1800 - x

Probability of Picking Defective = \(\frac{Total Defective}{ Total}\) [i.e. = \(\frac{x}{ 1800}\) ]
Probability of Picking Non-Defective = \(\frac{Total Non-Defective}{ Total}\) [i.e. = \(\frac{1800-x}{ 1800}\) ]

\(\frac{Probability Of Picking Defective}{Probability Of Picking Non-Defective}\) = \(\frac{Total Defective}{ Total }\)/ \(\frac{Total Non-Defective}{ Total}\)
= \(\frac{Total Defective}{ Total Non-Defective}\) = \(\frac{x}{ 1800-x}\) = \(\frac{1}{9}\) [ Given]

=> 9x = 1800 - x
=> 10x = 1800
=> x = 180

So, answer will be C
Hope it helps!
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Re: A shipment consists of 1,800 parts, some of which are defect [#permalink] New post   25 Jul 2020, 00:13
Is my approach correct?
1/9 * (1-1/9)
1/9*8/9
8/81 = 0.098
0.098 * 1800 = 176.4 approx which is close to 180
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Re: A shipment consists of 1,800 parts, some of which are defect [#permalink] New post   25 Jul 2020, 00:18
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Can you elaborate 1/9 * (1-1/9)

Are you saying 1/9 * P(Non-Defective)
So, P(Non-Defective) you are assuming is (1-1/9) that means 1 - P(Defective) = 1 - 1/9
So, you assuming P(Defective) = 1/9 ?
I would not recommend taking that assumption even if the answer is approximately correct.

Hope it helps!
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Re: A shipment consists of 1,800 parts, some of which are defect [#permalink] New post   25 Jul 2020, 02:13
BrushMyQuant wrote:
Can you elaborate 1/9 * (1-1/9)

Are you saying 1/9 * P(Non-Defective)
So, P(Non-Defective) you are assuming is (1-1/9) that means 1 - P(Defective) = 1 - 1/9
So, you assuming P(Defective) = 1/9 ?
I would not recommend taking that assumption even if the answer is approximately correct.

Hope it helps!


The question stem says:
The probability of it being defective is 1/9 the probability that it is not defective

being defective: 1/9
of the probability being non defective: Non defective would be 1-1/9

so if you translate Eng into Maths: The probability of it being defective is 1/9 the probability that it is not defective
: 1/9 * (1-1/9)

or maybe I have not understood it correctly
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Re: A shipment consists of 1,800 parts, some of which are defect [#permalink] New post   25 Jul 2020, 03:08
@Farina

I get confusion now. The question says "the probability of it being defective is 1/9 the probability that it is not defective"

They actually wanted to say that "the probability of it being defective is 1/9th of the probability that it is not defective"

@Carcass: Do we want to edit the question to have this specified please?

Hope it helps!
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Re: A shipment consists of 1,800 parts, some of which are defect [#permalink] New post   25 Jul 2020, 03:13
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Sorry Guys

I should add the cardinal th ??

Is it this ?' But the question is correct as is transcribed ??

Will see what @GreenlightTestPrep says
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Re: A shipment consists of 1,800 parts, some of which are defect [#permalink] New post   25 Jul 2020, 05:01
BrushMyQuant wrote:
@Farina

I get confusion now. The question says "the probability of it being defective is 1/9 the probability that it is not defective"

They actually wanted to say that "the probability of it being defective is 1/9th of the probability that it is not defective"

@Carcass: Do we want to edit the question to have this specified please?

Hope it helps!


If you would add "of" my solution would be correct I think :) Hence the confusion remains
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Re: A shipment consists of 1,800 parts, some of which are defect [#permalink] New post   25 Jul 2020, 06:06
1
"the probability of it being defective is 1/9th of the probability that it is not defective"
This does not mean that Probability of Defective is 1/9
This means that probability of defective = 1/9th of the probability of non-Defective

Ex: If probability of non-defective is 9/10 then probability of defective is 1/9 of 9/10 = 1/10

Hope it helps!
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Re: A shipment consists of 1,800 parts, some of which are defect [#permalink] New post   25 Jul 2020, 06:09
BrushMyQuant wrote:
"the probability of it being defective is 1/9th of the probability that it is not defective"
This doe not mean that Probability of Defective is 1/9
This means that probability of defective = 1/9th of the probability of non-Defective

Ex: If probability of non-defective is 9/10 then probability of defective is 1/9 of 9/10 = 1/10

Hope it helps!

I got it now, thanks a lot for your help. It was certainly the problem of my understanding of language
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Re: A shipment consists of 1,800 parts, some of which are defect [#permalink] New post   25 Jul 2020, 06:17
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To be honest I did not get the point to edit the question because for me there was nothing wrong in the wording :|
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Re: A shipment consists of 1,800 parts, some of which are defect [#permalink] New post   25 Jul 2020, 06:52
Now that I re-read it and re-re-re-read it then it sounds okay I guess
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Re: A shipment consists of 1,800 parts, some of which are defect [#permalink] New post   25 Jul 2020, 07:26
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Carcass wrote:
A shipment consists of 1,800 parts, some of which are defective. If a part is chosen from the shipment at random, the probability of it being defective is 1/9 the probability that it is not defective. How many of the parts in the shipment are defective?
(A) 90
(B) 120
(C) 180
(D) 200
(E) 900


The probability of it (the part) being defective is 1/9 the probability that it is not defective
This does NOT mean P(getting a defective part) = 1/9

Let x = the probability that the part is defective
So, 1 - x = the probability that the part is NOT defective

From the given information we can write: (probability of defective part) = (1/9)(probability of NON-defective part)
So we can write: x = (1/9)(1 - x)
To eliminate the fractions, multiply both sides by 9 to get: 9x = 1 - x
Add x to both sides: 10x = 1
Divide both sides by 10 to get: x = 1/10

So, P(electing a defective part) = 1/10
In other words, 1/10 of all parts are defective.

If there are 1800 parts in total, then the number of defective parts = 1/10 of 1800 = 180

Answer: C

Cheers,
Brent
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Re: A shipment consists of 1,800 parts, some of which are defect [#permalink] New post   25 Jul 2020, 08:43
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BrushMyQuant wrote:
Now that I re-read it and re-re-re-read it then it sounds okay I guess


Exactly
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Re: A shipment consists of 1,800 parts, some of which are defect [#permalink] New post   25 Jul 2020, 08:44
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GreenlightTestPrep wrote:
Carcass wrote:
A shipment consists of 1,800 parts, some of which are defective. If a part is chosen from the shipment at random, the probability of it being defective is 1/9 the probability that it is not defective. How many of the parts in the shipment are defective?
(A) 90
(B) 120
(C) 180
(D) 200
(E) 900


The probability of it (the part) being defective is 1/9 the probability that it is not defective
This does NOT mean P(getting a defective part) = 1/9

Let x = the probability that the part is defective
So, 1 - x = the probability that the part is NOT defective

From the given information we can write: (probability of defective part) = (1/9)(probability of NON-defective part)
So we can write: x = (1/9)(1 - x)
To eliminate the fractions, multiply both sides by 9 to get: 9x = 1 - x
Add x to both sides: 10x = 1
Divide both sides by 10 to get: x = 1/10

So, P(electing a defective part) = 1/10
In other words, 1/10 of all parts are defective.

If there are 1800 parts in total, then the number of defective parts = 1/10 of 1800 = 180

Answer: C

Cheers,
Brent



Thank you Sir for the explanation
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Re: A shipment consists of 1,800 parts, some of which are defect [#permalink] New post   25 Jul 2020, 09:06
Farina wrote:
Is my approach correct?
1/9 * (1-1/9)
1/9*8/9
8/81 = 0.098
0.098 * 1800 = 176.4 approx which is close to 180


Yes, 176.4 is close to 180, but the question isn't asking us to find the "approximate" number of defective parts.

In your solution, what does "1/9*8/9" represent?
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Re: A shipment consists of 1,800 parts, some of which are defect [#permalink] New post   26 Jul 2020, 00:45
GreenlightTestPrep wrote:
Farina wrote:
Is my approach correct?
1/9 * (1-1/9)
1/9*8/9
8/81 = 0.098
0.098 * 1800 = 176.4 approx which is close to 180


Yes, 176.4 is close to 180, but the question isn't asking us to find the "approximate" number of defective parts.

In your solution, what does "1/9*8/9" represent?


I considered 1/9 as defective and 1-1/9 as non defective. You have already addressed in your answer that this assumption is wrong.
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Re: A shipment consists of 1,800 parts, some of which are defect [#permalink]
26 Jul 2020, 00:45
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