Author 
Message 
TAGS:

Hide Tags

Director
Joined: 01 May 2007
Posts: 793

If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink]
Show Tags
16 Jul 2007, 14:25
17
This post was BOOKMARKED
Question Stats:
65% (00:54) correct 35% (00:58) wrong based on 685 sessions
HideShow timer Statistics
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}, what is the probability that xy will be even? A. 1/6 B. 1/3 C. 1/2 D. 2/3 E. 5/6
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 17 Sep 2013, 06:23, edited 1 time in total.
Renamed the topic, edited the question and added the OA.



Manager
Joined: 24 Jun 2006
Posts: 129

2
This post received KUDOS
7
This post was BOOKMARKED
it should be D
even x even =1/2*1/3
evenx odd= 1/2* 2/3
odd*even= 1/2*1/3
P= 1/6+ 2/6+ 1/6= 2/3



Director
Joined: 12 Jun 2006
Posts: 529

Re: PS  Probability [#permalink]
Show Tags
16 Jul 2007, 15:03
1
This post was BOOKMARKED
jimmyjamesdonkey wrote: Q: 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}, what is the probability that xy will be even?
A) 1/6 B) 1/3 C) 1/2 D) 2/3 E) 5/6
there are 12 different possibilities:
4C1 = 4
3C1 = 3
4(3) = 12
there's a 2/3 chance of set {5,6,7} giving us an odd # and there is a 1/2 chance of set {1,2,3,4} giving us an odd#. if only odd * odd = odd, there is a 1/3 = (2/3)*(1/2) chance of getting an odd product. therefore, there's a 8/12 ((1/3)*12 = 4) chance of getting an even product. 8/12 = 4/6 = 2/3



Director
Joined: 01 May 2007
Posts: 793

8
This post received KUDOS
4
This post was BOOKMARKED
OA is 2/3. Good job all. I actually got this wrong, but here is a great tip. I think everytime you see a probability problem, look at what it is asking, and then find the opposite of it.
For example, it is asking you to find the prob of xy being even...instead find the prob of it being ODD.
How is it odd? If x and y are both ODD.
Prob of x being odd: 1/2
prob of y being odd: 2/3
Prob of x and y being ODD: 1/2 * 2/3 = 1/3
Now 1  1/3 = 2/3..our answer.
I find that on all the OG problems dealing with prob, looking at it in reverse seems to bring you to a answer quicker. Anyone agree with that?



Intern
Joined: 17 Jun 2012
Posts: 1
Location: India
GMAT Date: 03062014
WE: Supply Chain Management (Transportation)

Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink]
Show Tags
23 Jan 2014, 13:01
I think we can use combinations too, to arrive at the answer.
The total number of combinations is 12 (4C1 for X * 3C1 for Y). The possibilities for having XY as even are:
1) when X is 1, Y has to be 6. That makes it 1C1*1C1 2) when X is 2, Y can take 5,6,7. This would be 1C1*3C1 3) when X is 3, Y can take only 6. So, this would mean 1C1*1C1 4) when X is 4, Y can take 5,6,7. That would be 1C1*3C1
So, 1C1*1C1 + 1C1*3C1 + 1C1*1C1 + 1C1*3C1 is divided by 4C1*3C1, i.e when 1 + 3 +1 + 3 is divided by 4*3 we get 2/3.
Please let me know if I am wrong.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7942
Location: Pune, India

Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink]
Show Tags
23 Jan 2014, 20:02
2
This post received KUDOS
Expert's post
3
This post was BOOKMARKED
jimmyjamesdonkey 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}, what is the probability that xy will be even?
A. 1/6 B. 1/3 C. 1/2 D. 2/3 E. 5/6 You can also use the sets formula: P(xy is even) = P(x is even) + P(y is even)  P(Both x and y are even) (We subtract this to get rid of the double counting) P(xy is even) = 2/4 + 1/3  (2/4)(1/3) = 2/3 You can do many questions using the same concept. Check out this post for more on this: http://www.veritasprep.com/blog/2012/01 ... ecouples/
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



SVP
Joined: 08 Jul 2010
Posts: 1955
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink]
Show Tags
23 Jul 2015, 05:47
1
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
jimmyjamesdonkey 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}, what is the probability that xy will be even?
A. 1/6 B. 1/3 C. 1/2 D. 2/3 E. 5/6 Method1xy will be even when 1) x is even and y is odd, Probability of x even is (2/4) and Probability of y odd is (2/3), so Probability of Case(1) = (2/4)*(2/3) = (4/12) 2) x is Odd and y is Even, Probability of x Odd is (2/4) and Probability of y Even is (1/3), so Probability of Case(2) = (2/4)*(1/3) = (2/12) 3) x is even and y is Even, Probability of x even is (2/4) and Probability of y Even is (1/3), so Probability of Case(1) = (2/4)*(1/3) = (2/12) Total Favorable Probability = (4/12)+(2/12)+(2/12) = (8/12) = 2/3 Answer: option D Method2Unfavorable case is when x and y are both odd, Unfavorable Probability = (2/4)*(2/3) = 1/3 i.e. favorable probability = 1(1/3) = 2/3 Answer: option D
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Senior Manager
Joined: 28 Jun 2015
Posts: 299
Concentration: Finance
GPA: 3.5

Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink]
Show Tags
23 Jul 2015, 06:30
1
This post received KUDOS
Let A = {1,2,3,4}, B = {5,6,7}. Total mappings from A>B = 4 * 3 = 12. Number of mappings from A>B where A = {2,4} and B = {6}: 2 * 1 = 2 [even > even] Number of mappings from A>B where A = {1,3} and B = {6}: 2 * 1 = 2 [odd > even] Number of mappings from A>B where A = {2,4} and B = {5,7}: 2 * 2 = 4 [even > odd] Total favourable events = 2+2+4 = 8. Probability = 8/12 = 2/3. Ans (D).
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.



Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 1912
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE: Information Technology (Consulting)

Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink]
Show Tags
05 Oct 2015, 00:33
Set A={1, 2, 3, 4} Set B={5, 6, 7} For the product xy to be even , atleast one of the selected numbers should be even . Method 1 = Prob(x is even and y is even) + Prob(x is even and y is odd) + Prob(x is odd and y is even) Method 2=Prob(Favourable outcomes)= 1  Prob(Unfavourable outcomes) =1 Prob(x is Odd and y is Odd) The method of finding the unfavourable outcomes and subtracting the result from 1 will be quicker .
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it.  Henry Ford The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long +1 Kudos if you find this post helpful



NonHuman User
Joined: 09 Sep 2013
Posts: 13807

Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink]
Show Tags
20 Oct 2016, 02:01
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Manager
Joined: 03 Jan 2017
Posts: 193

Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink]
Show Tags
23 Mar 2017, 04:02
my approach was to start apply 1xy (odd). As odd multiply can be only in case x and y are odd.
X set: 2/4 Y set: 2/3 2/4 and 2/3 = 4/12 1 4/12=8/12=2/3 Answer is D
Another approach: e*o=2/4*2/3 o*e=2/4*1/3 e*e=2/4*1/3 8/12 or 2/3



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1975

Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink]
Show Tags
27 Mar 2017, 10:49
jimmyjamesdonkey 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}, what is the probability that xy will be even?
A. 1/6 B. 1/3 C. 1/2 D. 2/3 E. 5/6 In order for xy to be even, at least one of the values of x and y needs to be even. We know that (1) even x even = even and (2) even x odd = even, and (3) odd x even = even. Case 1. Both x and y are even. The probability that x is even is 2/4 = 1/2 , and the probability that y is even is ⅓; thus, the probability that x and y will both be even is 1/2 x 1/3 = 1/6 Case 2. x is even and y is odd. The probability that x is even is 1/2, and the probability that y is odd is ⅔; thus, the probability that x is even and y is odd is 1/2 x 2/3 = 2/6 = 1/3. Case 3. x is odd and y is even. The probability that x is odd is ½, and the probability that y is even is ⅓; thus, the probability that x is odd and y is even is 1/2 x 1/3 = 1/6. Thus, the total probability that the product xy will be even is 1/6 + 1/3 + 1/6 = 1/6 + 2/6 + 1/6 = 4/6 = 2/3. Answer: D
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 16 Sep 2017
Posts: 10

Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink]
Show Tags
18 Sep 2017, 05:48
A noob question, if one set gives even does other set even matter as product would be even.
Probability to get even out of 1,2,3,4  Is 2/4 or 1/2
Probability to get even out of 5,6,7  Is 1/3
Shouldnt it be then
Pset1(even)*1(as other set doesn't matteranswer would be even) + Pset2(even)*1 =1/2+1/3.
Posted from my mobile device



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7942
Location: Pune, India

Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink]
Show Tags
18 Sep 2017, 21:10
Anantz wrote: A noob question, if one set gives even does other set even matter as product would be even.
Probability to get even out of 1,2,3,4  Is 2/4 or 1/2
Probability to get even out of 5,6,7  Is 1/3
Shouldnt it be then
Pset1(even)*1(as other set doesn't matteranswer would be even) + Pset2(even)*1 =1/2+1/3.
Posted from my mobile device Here is the problem with this solution: Pset1(even)*1 includes the probability that both elements are even. Pset2(even)*1 also includes the probability that both elements are even. So a case such as 2, 6 is counted twice. We need to remove once the probability that both are even. Pset1(even)*Pset2(even) = (1/2)*(1/3) = 1/6 So to get the answer, 1/2 + 1/3  1/6 = 2/3 I have discussed the same thing here: https://gmatclub.com/forum/ifxistob ... l#p1321459
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Intern
Joined: 16 Sep 2017
Posts: 10

Re: If x is to be chosen at random from the set {1, 2, 3, 4} and [#permalink]
Show Tags
18 Sep 2017, 21:26
2&6 and 6&2 getting in twice.
Got it thank you.
Posted from my mobile device




Re: If x is to be chosen at random from the set {1, 2, 3, 4} and
[#permalink]
18 Sep 2017, 21:26






