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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, 07:09
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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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C

Originally posted by Bunuel on 10 Jun 2021, 08:15.
Last edited by chetan2u on 02 Jul 2021, 07:09, edited 1 time in total.
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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, 07:08
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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

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

C
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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, 23:36
=((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, 08:22.
Last edited by sajjad1995 on 21 Jun 2021, 23:36, edited 1 time in total.
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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, 04:58
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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 \(\frac{12}{41}\)

Originally posted by MathRevolution on 10 Jun 2021, 08:54.
Last edited by MathRevolution on 21 Jun 2021, 04:58, edited 1 time in total.
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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, 16:43
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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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Re: Three companies P, Q and R supply 20%, 30% and 50% of the books to a [#permalink] New post   20 Jun 2021, 22:03
Hi MathRevolution,

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

Maybe I am missing something.

Thanks.
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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, 05:00
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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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Re: Three companies P, Q and R supply 20%, 30% and 50% of the books to a [#permalink] New post   21 Jun 2021, 05:00
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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
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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, 05:01
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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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Re: Three companies P, Q and R supply 20%, 30% and 50% of the books to a [#permalink] New post   21 Jun 2021, 23:39
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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Re: Three companies P, Q and R supply 20%, 30% and 50% of the books to a [#permalink] New post   11 Dec 2023, 23:17
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