GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 12 Nov 2018, 20:49

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • Essential GMAT Time-Management Hacks

     November 14, 2018

     November 14, 2018

     07:00 PM PST

     08:00 PM PST

    Join the webinar and learn time-management tactics that will guarantee you answer all questions, in all sections, on time. Save your spot today! Nov. 14th at 7 PM PST
  • $450 Tuition Credit & Official CAT Packs FREE

     November 15, 2018

     November 15, 2018

     10:00 PM MST

     11:00 PM MST

    EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)

A certain junior class has 1,000 students and a certain

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
Joined: 23 Jan 2008
Posts: 104
A certain junior class has 1,000 students and a certain  [#permalink]

Show Tags

New post Updated on: 26 Dec 2015, 08:18
14
51
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

60% (01:11) correct 40% (01:41) wrong based on 1656 sessions

HideShow timer Statistics

A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected at will be a sibling pair?

A. 3/40,000
B. 1/3,600
C. 9/2,000
D. 1/60
E. 1/15

Originally posted by blog on 23 Jan 2008, 11:55.
Last edited by NoHalfMeasures on 26 Dec 2015, 08:18, edited 3 times in total.
Added the OA
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50544
Re: A certain junior class has 1,000 students and a certain  [#permalink]

Show Tags

New post 09 Sep 2010, 20:27
27
17
blog wrote:
A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs , each consisting of 1 junior and 1 senior. If i student is to be selected at random from each class, what is the probability that the 2 students selected at will be a sibling pair?

A. 3/40,000
B. 1/3,600
C. 9/2,000
D. 1/60
E. 1/15


There are 60 siblings in junior class and 60 their pair siblings in the senior class. We want to determine probability of choosing one sibling from junior class and its pair from senior.

What is the probability of choosing ANY sibling from junior class? \(\frac{60}{1000}\) (as there are 60 of them).

What is the probability of choosing PAIR OF CHOSEN SIBLING in senior class? As in senior class there is only one pair of chosen sibling it would be \(\frac{1}{800}\) (as there is only one sibling pair of chosen one).

So the probability of that the 2 students selected will be a sibling pair is: \(\frac{60}{1000}*\frac{1}{800}=\frac{3}{40000}\)

Answer: A.

This problem can be solved in another way:

In how many ways we can choose 1 person from 1000: \(C^1_{1000}=1000\);
In how many ways we can choose 1 person from 800: \(C^1_{800}=800\);
So total # of ways of choosing 1 from 1000 and 1 from 800 is \(C^1_{1000}*C^1_{800}=1000*800\) --> this is total # of outcomes.

Let’s count favorable outcomes: 1 from 60 - \(C^1_{60}=60\);
The pair of the one chosen: \(C^1_1=1\)
So total # of favorable outcomes is \(C^1_{60}*C^1_1=60\)

\(Probability=\frac{# \ of \ favorable \ outcomes}{Total \ # \ of \ outcomes}=\frac{60}{1000*800}=\frac{3}{40000}\).

Answer: A.

Let’s consider another example:
A certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 60 siblings of four children, each consisting of 2 junior and 2 senior (I’m not sure whether it’s clear, I mean there are 60 brother and sister groups, total 60*4=240, two of each group is in the junior class and two in the senior). If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?

The same way here:

What is the probability of choosing ANY sibling from junior class? 120/1000 (as there are 120 of them).
What is the probability of choosing PAIR OF CHOSEN SIBLING in senior class? As in senior class there is only two pair of chosen sibling it would be 2/800 (as there is only one sibling pair of chosen one).

So the probability of that the 2 students selected will be a sibling pair is: 120/1000*2/800=3/10000

Another way:
In how many ways we can choose 1 person from 1000=1C1000=1000
In how many ways we can choose 1 person from 800=1C800=800
So total # of ways of choosing 1 from 1000 and 1 from 800=1C1000*1C800=1000*800 --> this is our total # of outcomes.

Favorable outcomes:
1 from 120=120C1=120
The pair of the one chosen=1C2=2
So total favorable outcomes=120C1*1C2=240

Probability=Favorable outcomes/Total # of outcomes=240/(1000*800)=3/10000

Also discussed at: probability-85523.html?hilit=certain%20junior%20class#p641153
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Community Reply
Director
Director
User avatar
Joined: 12 Jul 2007
Posts: 845
Re: A certain junior class has 1,000 students and a certain  [#permalink]

Show Tags

New post 23 Jan 2008, 12:10
30
6
Image

Answer A

Let's say you're picking out of the Junior class first and the senior class second (although the order doesn't make any difference). There are 1000 juniors and 60 of them have a sibling in the senior class, so you have a Image shot of choosing one of the siblings. Then you move onto the senior class. There are 800 seniors and only one sibling of the person you chose from the junior class. Thus, you have a Image chance of choosing the sibling.

Multiply the two equations together and simplify...and there's your answer.
General Discussion
Intern
Intern
User avatar
Joined: 03 Jan 2008
Posts: 7
Re: A certain junior class has 1,000 students and a certain  [#permalink]

Show Tags

New post 23 Jan 2008, 12:24
Hi,
Great logic. But mez confused that the "1" sibling you've picked from the senior class is from the entire 800 and not from the 60 possible siblings in the senior class.

Does 1/800 imply picking 1 in 60 in this context?
Director
Director
User avatar
Joined: 12 Jul 2007
Posts: 845
Re: A certain junior class has 1,000 students and a certain  [#permalink]

Show Tags

New post 23 Jan 2008, 12:30
5
You have already chosen 1 of the 60 siblings in the junior class. Now that one person is chosen there is only 1 way to choose that persons sibling in the senior class. If you used out of 60 for both classes you would just be finding the probability of finding two people WITH siblings, not necessarily two people who ARE siblings.
Intern
Intern
User avatar
Joined: 03 Jan 2008
Posts: 7
Re: A certain junior class has 1,000 students and a certain  [#permalink]

Show Tags

New post 23 Jan 2008, 13:32
17
2
Hi again.
Thanks for the post.

I do know the stuff you were saying... chk this one -

Total no of pairs available:
1000 * 800 = 800,000

Total no of sibling pairs:
60

So, prob of pickin pair from the lot:
60/800000 = 3/40000

Ans: A :-D
Intern
Intern
avatar
Joined: 06 May 2008
Posts: 26
Re: A certain junior class has 1,000 students and a certain  [#permalink]

Show Tags

New post 17 May 2009, 19:24
10
1
Another way to view this problem:

Probability to get a sibling member on junior class=P1=60/1.000
Probability to get a sibling member on senior class=P2=60/800
Probability to get a sibling pair on all sibling pairs=P3=1/60
Probability that the 2 students selected at will be a sibling pair=P4

P4=P1*P2*P3=(60/1.000)*(60/800)*(1/60)=3/40.000
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50544
A certain junior class has 1,000 students and a certain  [#permalink]

Show Tags

New post 12 Dec 2009, 08:50
6
6

22. Probability



For more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
User avatar
Joined: 22 Dec 2009
Posts: 309
GMAT ToolKit User
Re: A certain junior class has 1,000 students and a certain  [#permalink]

Show Tags

New post 14 Feb 2010, 09:16
5
blog wrote:
A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs , each consisting of 1 junior and 1 senior. If i student is to be selected at random from each class, what is the probability that the 2 students selected at will be a sibling pair?

A. 3/40,000
B. 1/3,600
C. 9/2,000
D. 1/60
E. 1/15


No of ways of choosing 1 sibling pair out of 60 pairs = 60c1
No of ways of choosing 1 student from each class = 1000c1 x 800c1

Therefore probability of having 2 students choosen as a sibling pair = 60c1 / (1000c1 x 800c1) = 60 / (1000 x 800) = 3 / 40000 = A
_________________

Cheers!
JT...........
If u like my post..... payback in Kudos!! :beer

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice|
|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|


~~Better Burn Out... Than Fade Away~~

Intern
Intern
avatar
Joined: 01 Jul 2010
Posts: 42
Schools: LBS, Harvard, Booth, Stanford, ISB, NTU
WE 1: S/W Engineer
A certain junior class has 1000 students and a certain  [#permalink]

Show Tags

New post Updated on: 14 Feb 2012, 21:48
9
9
A certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?

A. 3/40000
B. 1/3600
C. 9/2000
D. 1/60
E. 1/15

My explanation is:

Total 60 students are siblings, out of which 30 are from Junior class and 30 are from senior class.
Hence prob of selecting 1 student from senior who is a sibling is 30C1/800C1, similarly, selecting one student from Junior who is a sibling is 30C1/1000C1.
Since selecting 2 ppl from 2 sets, the events are independent, total probability is : 30/800+ 30/1000.
Simplifying, I get 1/15.

Please tell me where I'm going wrong..

Originally posted by jananijayakumar on 13 Aug 2010, 02:15.
Last edited by Bunuel on 14 Feb 2012, 21:48, edited 1 time in total.
Edited the question
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50544
A certain junior class has 1000 students and a certain  [#permalink]

Show Tags

New post 13 Aug 2010, 02:33
9
4
First of all we have 60 siblings pairs, so there are 60 siblings in junior class and 60 siblings in senior class.

Next: the question ask "what is the probability that the 2 students selected will be a sibling pair", so the probability that they will be siblings of each other.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 18 Aug 2010
Posts: 1
Re: A certain junior class has 1,000 students and a certain  [#permalink]

Show Tags

New post 03 Nov 2010, 11:43
1
Hi Bunuel,

You have selected first from junior section and then from senior section(first method).
But I have a doubt,its not mentioned anywhere that we have to pick first fro.m junior sec and then from senior sec.
Likewise we have freedom to select first from senior section and then from junior section.
So prob = 60/1000 * 60/800*1/60 + 60/800*60/1000*1/60
= 3/40000 +3/40000
= 6/40000 (Ans)

Please correct me where I am going wrong?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50544
Re: A certain junior class has 1,000 students and a certain  [#permalink]

Show Tags

New post 03 Nov 2010, 12:40
5
diptich12 wrote:
Hi Bunuel,

You have selected first from junior section and then from senior section(first method).
But I have a doubt,its not mentioned anywhere that we have to pick first fro.m junior sec and then from senior sec.
Likewise we have freedom to select first from senior section and then from junior section.
So prob = 60/1000 * 60/800*1/60 + 60/800*60/1000*1/60
= 3/40000 +3/40000
= 6/40000 (Ans)

Please correct me where I am going wrong?


Sibling pair (\(a_{junior}\), \(a_{senior}\)) is the same pair as (\(a_{senior}\), \(a_{junior}\)) and with your approach you are counting the probability of selecting each such pair twice.

Sometimes for probability questions it's easy to check whether your approach is right by simplifying the problem. Basically you are saying that the probability is twice as high (instead of A. \(\frac{3}{40000}\), you are saying it's \(\frac{6}{40000}\)).

Consider there is 1 sibling pair, 1 in junior class, with total of 3 students and another in senior class, with total of 2 students. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected at will be a sibling pair?

With my approach the answer would be \(\frac{1}{3}*\frac{1}{2}=\frac{1}{6}\) (there are 6 pairs possible and there is only 1 sibling pair). To check whether this answer is correct you can easily list all possible pairs;
With your approach the answer would be: \(\frac{1}{3}*\frac{1}{2}+\frac{1}{2}*\frac{1}{3}=\frac{2}{6}\) , which is not correct. Basically with this approach you are doublecounting the same pair.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

VP
VP
User avatar
G
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1496
GMAT 1: 780 Q51 V48
GRE 1: Q800 V740
Re: A certain junior class has 1000 students and a certain senio  [#permalink]

Show Tags

New post 13 Apr 2012, 04:14
Probability = Number of ways to select 1 junior and 1 senior such that they make a sibling pair / number of ways to select 1 junior and 1 senior

= 60 / (1000*800)
= 60 / 800000
= 3 / 40000

or Option (A).
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Top MBA Admissions Consulting | Top MiM Admissions Consulting

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

Intern
Intern
avatar
Joined: 07 Jan 2013
Posts: 36
Location: India
Concentration: Finance, Strategy
GMAT 1: 570 Q46 V23
GMAT 2: 710 Q49 V38
GPA: 2.9
WE: Information Technology (Computer Software)
Reviews Badge
Re: A certain junior class has 1,000 students and a certain  [#permalink]

Show Tags

New post 23 Jul 2013, 18:22
i just wanted to validate this answer the other way around i,e to find the no. of ways at least one sibling or no sibling is present in the chosen 2 members and then subtracting from 1 i.e

Req prob =1- (prob of one sibling chosen from either class) + no sibling chosen from either class
= 1-(prob of one sibling from junior) + (prob of one siblng from senior ) + (no sibling)
= 1-\((\frac{60}{1000}*\frac{799}{800})+(\frac{60}{800}*\frac{999}{1000})+(\frac{740}{800}*\frac{940}{1000})\)


which is coming out to be -ve which obviously is wrong ,, i want to know as to what i am adding extra as a result the answer is -ve
_________________

Help with Kudos if I add to your knowledge realm.

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50544
Re: A certain junior class has 1,000 students and a certain  [#permalink]

Show Tags

New post 23 Jul 2013, 22:04
1
adg142000 wrote:
i just wanted to validate this answer the other way around i,e to find the no. of ways at least one sibling or no sibling is present in the chosen 2 members and then subtracting from 1 i.e

Req prob =1- (prob of one sibling chosen from either class) + no sibling chosen from either class
= 1-(prob of one sibling from junior) + (prob of one siblng from senior ) + (no sibling)
= 1-\((\frac{60}{1000}*\frac{799}{800})+(\frac{60}{800}*\frac{999}{1000})+(\frac{740}{800}*\frac{940}{1000})\)


which is coming out to be -ve which obviously is wrong ,, i want to know as to what i am adding extra as a result the answer is -ve


It should be: \(1-(\frac{60}{1000}*\frac{799}{800}+\frac{940}{1000}*1)=\frac{3}{40000}\)

\(\frac{60}{1000}*\frac{799}{800}\) --> p(sibling)*p(any but sibling pair)
\(\frac{940}{1000}*1\) --> p(not sibling)*p(any)

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8521
Location: Pune, India
Re: A certain junior class has 1,000 students and a certain  [#permalink]

Show Tags

New post 30 Sep 2013, 01:35
2
1
blog wrote:
A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs, each consisting of 1 junior and 1 senior. If i student is to be selected at random from each class, what is the probability that the 2 students selected at will be a sibling pair?

A. 3/40,000
B. 1/3,600
C. 9/2,000
D. 1/60
E. 1/15


Quote:
Responding to a pm: Why doesn't order matter here?


Check out this post: http://www.veritasprep.com/blog/2013/08 ... er-matter/
It discusses a very similar situation.

Also, whether order matter or not depends on how you perceive it. In probability, you calculate P(A) = P(Favorable Outcomes)/P(Total Outcomes)

Where applicable, you can make the order matter in both numerator and denominator or not make it matter in both numerator and denominator. The answer will be the same.

This Question:

Order Matters:
Favorable outcomes = 60*1 + 60*1
Total outcomes = 1000*800 + 800*1000
P(A) = 3/40,000

Order doesn't matter:
Favorable outcomes = 60*1
Total outcomes = 1000*800
P(A) = 3/40,000

Another case: A bag has 4 balls - red, green, blue, pink (Equal probability of selecting each ball)
What is the probability that you pick two balls and they are red and green?

Order Matters:
Favorable outcomes = 2 (RG, GR)
Total outcomes = 4*3
P(A) = 1/6

Order doesn't matter:
Favorable outcomes = 1 (a red and a green)
Total outcomes = 4C2 = 6
P(A) = 1/6

Previous case: 2 red and 3 white balls. What is the probability that you pick two balls such that one is red and other is white?
In how many ways can you pick a red and a white ball? Here the probability of picking each ball is different. So we cannot cannot use our previous method. Here the probability of picking 2 red balls is not the same as that of picking a red and a white. Hence you have to consider the order to find the complete probability of picking a red and a white.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Manager
Manager
User avatar
Status: A mind once opened never loses..!
Joined: 05 Mar 2015
Posts: 210
Location: India
MISSION : 800
WE: Design (Manufacturing)
GMAT ToolKit User Premium Member
Re: A certain junior class has 1000 students and a certain  [#permalink]

Show Tags

New post 10 May 2015, 22:30
Bunuel wrote:
First of all we have 60 siblings pairs, so there are 60 siblings in junior class and 60 siblings in senior class.

Next: the question ask "what is the probability that the 2 students selected will be a sibling pair", so the probability that they will be siblings of each other.

Back to the question:

A certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?

A. 3/40000
B. 1/3600
C. 9/2000
D. 1/60
E. 1/15

There are 60 siblings in junior class and 60 their pair siblings in the senior class. We want to determine probability of choosing one sibling from junior class and its pair from senior.

What is the probability of choosing ANY sibling from junior class? \(\frac{60}{1000}\) (as there are 60 of them).

What is the probability of choosing PAIR OF CHOSEN SIBLING in senior class? As in senior class there is only one pair of chosen sibling it would be \(\frac{1}{800}\) (as there is only one sibling pair of chosen one).

So the probability of that the 2 students selected will be a sibling pair is: \(\frac{60}{1000}*\frac{1}{800}=\frac{3}{40000}\)

Answer: A.

This problem can be solved in another way:

In how many ways we can choose 1 person from 1000: \(C^1_{1000}=1000\);
In how many ways we can choose 1 person from 800: \(C^1_{800}=800\);
So total # of ways of choosing 1 from 1000 and 1 from 800 is \(C^1_{1000}*C^1_{800}=1000*800\) --> this is total # of outcomes.

Let’s count favorable outcomes: 1 from 60 - \(C^1_{60}=60\);
The pair of the one chosen: \(C^1_1=1\)
So total # of favorable outcomes is \(C^1_{60}*C^1_1=60\)

\(Probability=\frac{# \ of \ favorable \ outcomes}{Total \ # \ of \ outcomes}=\frac{60}{1000*800}=\frac{3}{40000} = \frac{60}{}\).

Answer: A.

Hope it helps.



Hi
Am not good at probability
plz clarify

Questions says 1 student is selected from each class
shouldn't it be like>>


\(Probability=\frac{60}{1000} * \frac{1}{800} OR \frac{60}{800} * \frac{1}{1000} = \frac{3}{20000}\).
_________________

Thank you

+KUDOS

> I CAN, I WILL <

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2173
Re: A certain junior class has 1000 students and a certain  [#permalink]

Show Tags

New post 10 May 2015, 23:25
2
dpo28 wrote:
Bunuel wrote:
First of all we have 60 siblings pairs, so there are 60 siblings in junior class and 60 siblings in senior class.

Next: the question ask "what is the probability that the 2 students selected will be a sibling pair", so the probability that they will be siblings of each other.

Back to the question:

A certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?

A. 3/40000
B. 1/3600
C. 9/2000
D. 1/60
E. 1/15

There are 60 siblings in junior class and 60 their pair siblings in the senior class. We want to determine probability of choosing one sibling from junior class and its pair from senior.

What is the probability of choosing ANY sibling from junior class? \(\frac{60}{1000}\) (as there are 60 of them).

What is the probability of choosing PAIR OF CHOSEN SIBLING in senior class? As in senior class there is only one pair of chosen sibling it would be \(\frac{1}{800}\) (as there is only one sibling pair of chosen one).

So the probability of that the 2 students selected will be a sibling pair is: \(\frac{60}{1000}*\frac{1}{800}=\frac{3}{40000}\)

Answer: A.

This problem can be solved in another way:

In how many ways we can choose 1 person from 1000: \(C^1_{1000}=1000\);
In how many ways we can choose 1 person from 800: \(C^1_{800}=800\);
So total # of ways of choosing 1 from 1000 and 1 from 800 is \(C^1_{1000}*C^1_{800}=1000*800\) --> this is total # of outcomes.

Let’s count favorable outcomes: 1 from 60 - \(C^1_{60}=60\);
The pair of the one chosen: \(C^1_1=1\)
So total # of favorable outcomes is \(C^1_{60}*C^1_1=60\)

\(Probability=\frac{# \ of \ favorable \ outcomes}{Total \ # \ of \ outcomes}=\frac{60}{1000*800}=\frac{3}{40000} = \frac{60}{}\).

Answer: A.

Hope it helps.



Hi
Am not good at probability
plz clarify

Questions says 1 student is selected from each class
shouldn't it be like>>


\(Probability=\frac{60}{1000} * \frac{1}{800} OR \frac{60}{800} * \frac{1}{1000} = \frac{3}{20000}\).


Hi dpo28,

The order of selecting the sibling does not matter here. Let me explain you why your probability equation is not correct. Assume a pair of siblings A & B where A is in the senior class & B is in the junior class. If you select A from the senior class first, you can only select B from the junior class to make it a sibling pair.

Alternatively, if you select B from the junior class first, you can only select A from the senior class to make it a sibling pair. Thus, in both the cases we have the same pair of siblings as our final selection :). Hence the order of selection of siblings does not matter which is what your probability equation is intending to convey.

Hope its clear!

Regards
Harsh
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Director
Director
User avatar
S
Joined: 17 Dec 2012
Posts: 629
Location: India
Re: A certain junior class has 1000 students and a certain  [#permalink]

Show Tags

New post 31 May 2017, 21:46
gurpreet07 wrote:
A certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?

A. 3/40000
B. 1/3600
C. 9/2000
D. 1/60
E. 1/15

1. Select a person from a class , say the senior class.
2. Probability that the student has a sibling is 60/800
3. Probability of selecting a person who has a sibling in the Junior class is 60/1000.
4. Probability that the person selected is the sibling is 1/60.
5. Final probability is 60/800*60/1000*1/60=3/40000
_________________

Srinivasan Vaidyaraman
Sravna Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

GMAT Club Bot
Re: A certain junior class has 1000 students and a certain &nbs [#permalink] 31 May 2017, 21:46

Go to page    1   2    Next  [ 23 posts ] 

Display posts from previous: Sort by

A certain junior class has 1,000 students and a certain

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.