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On the table, there are 10 mathematics books and 5 literature books

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On the table, there are 10 mathematics books and 5 literature books [#permalink]

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On the table, there are 10 mathematics books and 5 literature books. Jane takes one randomly, then Anna takes one book randomly. Finally, John takes one of remaining on the table. What is the probability that Jane and Anna take mathematics books and John takes literature books?

A. 18/91
B. 15/91
C. 7/45
D. 8/15
E. 45/91
[Reveal] Spoiler: OA

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Re: On the table, there are 10 mathematics books and 5 literature books [#permalink]

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New post 11 Dec 2016, 08:09
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Hi

Thanks for posting new questions.

\(P(math)*P(math)|math*P(lit)|math,math = \frac{10}{15} * \frac{9}{14} * \frac{5}{13} = \frac{15}{91}\)

Answer B.

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Re: On the table, there are 10 mathematics books and 5 literature books [#permalink]

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New post 11 Dec 2016, 11:13
nguyendinhtuong wrote:
On the table, there are 10 mathematics books and 5 literature books. Jane takes one randomly, then Anna takes one book randomly. Finally, John takes one of remaining on the table. What is the probability that Jane and Anna take mathematics books and John takes literature books?

A. 18/91
B. 15/91
C. 7/45
D. 8/15
E. 45/91


Probability that Jane takes out a mathematics book = \(\frac{10}{15}\)
Probability that Anna takes out a mathematics book = \(\frac{9}{14}\)
Probability that John takes out a mathematics book = \(\frac{5}{13}\)

So, the probability that Jane and Anna take mathematics books and John takes literature books is \(\frac{10}{15}\)*\(\frac{9}{14}\)*\(\frac{5}{13}\) = \(\frac{15}{91}\)

Hence, answer will be (B)

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Re: On the table, there are 10 mathematics books and 5 literature books [#permalink]

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New post 13 Dec 2016, 16:46
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nguyendinhtuong wrote:
On the table, there are 10 mathematics books and 5 literature books. Jane takes one randomly, then Anna takes one book randomly. Finally, John takes one of remaining on the table. What is the probability that Jane and Anna take mathematics books and John takes literature books?

A. 18/91
B. 15/91
C. 7/45
D. 8/15
E. 45/91


We are given that there are 10 math and 5 literature books. We need to determine the probability of Jane selecting a math book, then Anna selecting a math book, and then John selecting a literature book.

Since there are 15 total books and 10 math books, the probability of Jane selecting a math book is 10/15 = 2/3. Since there are now 14 books left, of which 9 are math books, the probability of Anna selecting a math book is 9/14. Finally, since there are 13 books left, of which 5 are literature books, the probability of John selecting a literature book is 5/13.

Thus, the final probability is: 2/3 x 9/14 x 5/13 = 1 x 3/7 x 5/13 = 15/91.

Answer: B
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Re: On the table, there are 10 mathematics books and 5 literature books [#permalink]

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I can't get the same answer using the Combinatorial approach, could anyone please show me how to use it to get the right answer?

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Re: On the table, there are 10 mathematics books and 5 literature books [#permalink]

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New post 16 Apr 2017, 10:00
Alarin101 wrote:
I can't get the same answer using the Combinatorial approach, could anyone please show me how to use it to get the right answer?


I don't think you can use combinatorial approach, because order matters in this question. They are very specific than Jane goes first, and then Ana, and then John.

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Re: On the table, there are 10 mathematics books and 5 literature books   [#permalink] 16 Apr 2017, 10:00
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