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Three companies P, Q and R supply 20%, 30% and 50% of the books to a
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Bunuel
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Three companies P, Q and R supply 20%, 30% and 50% of the books to a [#permalink] New post  Updated on: 02 Jul 2021, 06:09
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Three companies P, Q and R supply 20%, 30% and 50% of the books to a college. Past experience shows that 20%, 4% and 5% of the books produced by these companies are defective. If a book was found to be defective, what is the probability that the book was supplied by company Q?

(A) 8/77
(B) 10/77
(C) 12/77
(D) 17/77
(E) 19/77
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Originally posted by Bunuel on 10 Jun 2021, 07:15.
Last edited by chetan2u on 02 Jul 2021, 06:09, edited 1 time in total.
Edited
Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
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sajjad1995
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Re: Three companies P, Q and R supply 20%, 30% and 50% of the books to a [#permalink] New post  Updated on: 21 Jun 2021, 22:36
=((30/100)*(4/100))/(((20/100)*
(2/100))+((30/100)*(4/100))+
((50/100)*(5/100)))
= 12/41

Originally posted by sajjad1995 on 10 Jun 2021, 07:22.
Last edited by sajjad1995 on 21 Jun 2021, 22:36, edited 1 time in total.
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MathRevolution
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Re: Three companies P, Q and R supply 20%, 30% and 50% of the books to a [#permalink] New post  Updated on: 21 Jun 2021, 03:58
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P = supply = 0.20
Q = supply = 0.30
R = supply = 0.50

Defective from P: 0.02
Defective from Q: 0.04
Defective from R: 0.05


Only Q supplied: \(\frac{(0.30 * 0.04) }{ (0.20 * 0.02) + (0.30 * 0.04) + (0.50 * 0.05)} = \frac{0.012 }{ (0.004+0.012+0.025)} = \frac{0.012}{0.041} = \frac{12}{41}\)


Answer should be \(\frac{12}{41}\)
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Originally posted by MathRevolution on 10 Jun 2021, 07:54.
Last edited by MathRevolution on 21 Jun 2021, 03:58, edited 1 time in total.
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gvij2017
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Re: Three companies P, Q and R supply 20%, 30% and 50% of the books to a [#permalink] New post  10 Jun 2021, 15:43
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I could not understand the math behind 0.004+0.012+0.025= 0.077
How did you get it?

MathRevolution wrote:
P = supply = 0.20
Q = supply = 0.30
R = supply = 0.50

Defective from P: 0.02
Defective from Q: 0.04
Defective from R: 0.05


Only Q supplied: \(\frac{(0.30 * 0.04) }{ (0.20 * 0.02) + (0.30 * 0.04) + (0.50 * 0.05)} = \frac{0.012 }{ (0.004+0.012+0.025)} = \frac{0.012}{0.077} = \frac{12}{77}\)


Answer C
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Awa327
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Re: Three companies P, Q and R supply 20%, 30% and 50% of the books to a [#permalink] New post  20 Jun 2021, 21:03
Hi MathRevolution,

How is (0.004+0.012+0.025) = 0.077?

Maybe I am missing something.

Thanks.
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MathRevolution
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Re: Three companies P, Q and R supply 20%, 30% and 50% of the books to a [#permalink] New post  21 Jun 2021, 04:00
Expert Reply
gvij2017 wrote:
I could not understand the math behind 0.004+0.012+0.025= 0.077
How did you get it?

MathRevolution wrote:
P = supply = 0.20
Q = supply = 0.30
R = supply = 0.50

Defective from P: 0.02
Defective from Q: 0.04
Defective from R: 0.05


Only Q supplied: \(\frac{(0.30 * 0.04) }{ (0.20 * 0.02) + (0.30 * 0.04) + (0.50 * 0.05)} = \frac{0.012 }{ (0.004+0.012+0.025)} = \frac{0.012}{0.077} = \frac{12}{77}\)



Hello,

Thanks for pointing that out. I missed something in the denominator part and submitted the answer. Now, have edited it.

Thanks

Answer C

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MathRevolution
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Re: Three companies P, Q and R supply 20%, 30% and 50% of the books to a [#permalink] New post  21 Jun 2021, 04:00
Expert Reply
Awa327 wrote:
Hi MathRevolution,

How is (0.004+0.012+0.025) = 0.077?

Maybe I am missing something.

Thanks.


Hello,

Thanks for pointing that out. I missed something in the denominator part and submitted the answer. Now, have edited it.

Thanks
_________________
MathRevolution: The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting at $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online
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MathRevolution
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Re: Three companies P, Q and R supply 20%, 30% and 50% of the books to a [#permalink] New post  21 Jun 2021, 04:01
Expert Reply
sajjad1995 wrote:
=((30/100)*(4/100))/(((20/100)*
(2/100))+((30/100)*(4/100))+
((50/100)*(5/100)))
= 12/77
Hence, C is the answer.

Posted from my mobile device


Hello,

How denominator gives 77?

Thanks
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sajjad1995
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Re: Three companies P, Q and R supply 20%, 30% and 50% of the books to a [#permalink] New post  21 Jun 2021, 22:39
MathRevolution wrote:
sajjad1995 wrote:
=((30/100)*(4/100))/(((20/100)*
(2/100))+((30/100)*(4/100))+
((50/100)*(5/100)))
= 12/77
Hence, C is the answer.

Posted from my mobile device


Hello,

How denominator gives 77?

Thanks


I have calculated only numerator and ignored calculation for denominator. Sorry for that.
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chetan2u
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Re: Three companies P, Q and R supply 20%, 30% and 50% of the books to a [#permalink] New post  02 Jul 2021, 06:08
Expert Reply
Bunuel wrote:
Three companies P, Q and R supply 20%, 30% and 50% of the books to a college. Past experience shows that 2%, 4% and 5% of the books produced by these companies are defective. If a book was found to be defective, what is the probability that the book was supplied by company Q?

(A) 8/77
(B) 10/77
(C) 12/77
(D) 17/77
(E) 19/77



The question may have an error with one of the numbers.

Let the number of books be 20, 30 and 50.

1) 2% 20% of 20 books are defective =4
2) 4% of 30 books are defective = 1.2
3) 5% of 50 books are defective = 2.5

Total defective books = 4+1.2+2.5 = 7.7

\(P(Q_d)=\frac{1.2}{7.7}=\frac{12}{77}\)

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Re: Three companies P, Q and R supply 20%, 30% and 50% of the books to a [#permalink]
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