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# Two sets are defined as follows (m25#17)

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Two sets are defined as follows (m25#17) [#permalink]

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15 Feb 2012, 06:51
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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) $$\frac{2}{3}$$
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Last edited by Bunuel on 15 Oct 2012, 10:28, edited 1 time in total.
OA edited.
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Re: Two sets are defined as follows (m25#17) [#permalink]

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17 Feb 2012, 12:40
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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:

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 [ 15.37 KiB | Viewed 2097 times ]

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Mike McGarry
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Last edited by mikemcgarry on 15 Oct 2012, 13:07, edited 1 time in total.
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Re: Two sets are defined as follows (m25#17) [#permalink]

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07 Oct 2012, 04:07
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]

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15 Oct 2012, 10:23

i got 4/9...
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Re: Two sets are defined as follows (m25#17) [#permalink]

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15 Oct 2012, 10:29
Expert's post
sanjoo wrote:

i got 4/9...

OA for this question is 4/9 not 5/9.
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If a numer is taken from set X [#permalink]

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20 May 2013, 15:21
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
Math Expert
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Kudos [?]: 68804 [0], given: 9818

Re: If a numer is taken from set X [#permalink]

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20 May 2013, 15:24
Expert's post
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

Merging similar topics.

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Re: If a numer is taken from set X   [#permalink] 20 May 2013, 15:24
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# Two sets are defined as follows (m25#17)

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