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# If x is to be chosen at random from the set {1,2,3,4} and y

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Joined: 26 Feb 2011
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If x is to be chosen at random from the set {1,2,3,4} and y [#permalink]  01 Mar 2011, 08:32
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Difficulty:

45% (medium)

Question Stats:

76% (01:16) correct 24% (01:00) wrong based on 21 sessions
If x is to be chosen at random from the set {1,2,3,4} and y is to be chosen at random from the set {5,6,7}, whats the probability that xy will be even?

A. 1/6
B. 1/3
C. 1/2
D. 2/3
E. 5/6

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-is-to-be-chosen-at-random-from-the-set-1-2-3-4-and-167089.html
[Reveal] Spoiler: OA
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Math Expert
Joined: 02 Sep 2009
Posts: 28351
Followers: 4486

Kudos [?]: 45457 [0], given: 6761

Re: Set problem [#permalink]  01 Mar 2011, 08:42
Expert's post
Madelaine88 wrote:
If x is to be chosen at random from the set {1,2,3,4} and y is to be chosen at random from the set {5,6,7}, whats the probability that xy will be even?
A/ 1/6
B/ 1/3
C/ 1/2
D/ 2/3
E/ 5/6

The product to be even either one or both must be even, so:
P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/4*1/3=2/3;

Or: P(xy=even)=1-P(xy=odd)=1-2/4*2/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1.

Answer: D.
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Current Student
Joined: 23 Oct 2010
Posts: 386
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
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Kudos [?]: 194 [0], given: 73

Re: Set problem [#permalink]  17 Feb 2014, 01:15
If we take 6 from Set 2 , we can take any 4 numbers from set 1
If we take 2 from Set 1 , we can take any 2 numbers from set 2 (exclude 6, since u count it once)
If we take 4 from Set 1 , we can take any 2 numbers from set 2 (exclude 6, since u count it once)

so we have (4+2+2)/ (4c1*3c1)=2/3
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Math Expert
Joined: 02 Sep 2009
Posts: 28351
Followers: 4486

Kudos [?]: 45457 [0], given: 6761

Re: If x is to be chosen at random from the set {1,2,3,4} and y [#permalink]  17 Feb 2014, 01:21
Expert's post
OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-is-to-be-chosen-at-random-from-the-set-1-2-3-4-and-167089.html
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Re: If x is to be chosen at random from the set {1,2,3,4} and y   [#permalink] 17 Feb 2014, 01:21
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# If x is to be chosen at random from the set {1,2,3,4} and y

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