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Two sets are defined as follows (m25#17)

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CIO
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Two sets are defined as follows (m25#17) [#permalink] New post 15 Feb 2012, 05:51
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

66% (01:28) correct 33% (00:05) wrong based on 15 sessions
Two sets are defined as follows:
\begin{eqnarray*} X &=& (4, 5, 8)\\ Y &=& (-1, 1, 2)\\ \end{eqnarray*}

If a number is taken from set X at random and another number is taken from set Y at random, what is the probability that the sum of these numbers will be an even integer?

(A) \frac{2}{9}
(B) \frac{1}{3}
(C) \frac{4}{9}
(D) \frac{5}{9}
(E) \frac{2}{3}
[Reveal] Spoiler: OA

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Last edited by Bunuel on 15 Oct 2012, 09:28, edited 1 time in total.
OA edited.
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Re: Two sets are defined as follows (m25#17) [#permalink] New post 17 Feb 2012, 11:40
Expert's post
Hi, there. I'm happy to help with this.

Big idea #1:
(even) + (even) = even
(odd) + (odd) = even
but . . .
(odd) + (even) = odd

There are nine combinations here (any of the three of the first set with any of the three of the second set). The results are shown in the matrix attached (odds = green, evens = red).

Of the nine cases, five are odd.

[Reveal] Spoiler:
Therefore, the answer = C


Does this make sense? Please let me know if anyone reading this has any questions on what I've said.

Mike :)
Attachments

matrix of odd & even sums.JPG
matrix of odd & even sums.JPG [ 15.37 KiB | Viewed 1073 times ]


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Last edited by mikemcgarry on 15 Oct 2012, 12:07, edited 1 time in total.
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Re: Two sets are defined as follows (m25#17) [#permalink] New post 07 Oct 2012, 03:07
As mentioned above for getting even we have 2 options e+e or o+o

set X SET Y

Considering E+E (selecting even from both the set )

2C1(4,8) * 1C1(2) =2

Considering O+O (selecting even from both the set )
1C1(5) * 2C1(-1,1)=2

As both the cases are independent of each other we will add the possibilities i.e 2+2=4

Total cases = 3C1*3C1 =9

required probability = desired outcome /total outcome =4/9 Ans

Hope it helps!

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Re: Two sets are defined as follows (m25#17) [#permalink] New post 15 Oct 2012, 09:23
how can answer b 5/9??

i got 4/9...
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Re: Two sets are defined as follows (m25#17) [#permalink] New post 15 Oct 2012, 09:29
Expert's post
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If a numer is taken from set X [#permalink] New post 20 May 2013, 14:21
If a number is taken from set X at random and another number is taken from set Y at random, what is the probability that the sum of these numbers will be an even integer?

29
13
49
59
23
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Re: If a numer is taken from set X [#permalink] New post 20 May 2013, 14:24
Expert's post
Re: If a numer is taken from set X   [#permalink] 20 May 2013, 14:24
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