Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 01 Jul 2010
Posts: 51
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
13 Aug 2010, 03:15
3
This post received KUDOS
9
This post was BOOKMARKED
Question Stats:
68% (01:51) correct
32% (01:19) wrong based on 234 sessions
HideShow timer Statistics
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..
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 14 Feb 2012, 22:48, edited 1 time in total.
Edited the question



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: Probablility [#permalink]
Show Tags
13 Aug 2010, 03:33
6
This post received KUDOS
Expert's post
6
This post was BOOKMARKED
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 \(C^1_{60}*C^1_1=60\) \(Probability=\frac{# \ of \ favorable \ outcomes}{Total \ # \ of \ outcomes}=\frac{60}{1000*800}=\frac{3}{40000}\). Answer: A.Hope it helps.
_________________
New to the Math Forum? Please read this: 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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 01 Jul 2010
Posts: 51
Schools: LBS, Harvard, Booth, Stanford, ISB, NTU
WE 1: S/W Engineer

Re: Probablility [#permalink]
Show Tags
13 Aug 2010, 07:57
Ah... I missed the "sibling pair" word!! And my explanation was also wrong! Thanks buddy!



Senior Manager
Joined: 10 Nov 2010
Posts: 262
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19 GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)

Probability to select sibling [#permalink]
Show Tags
19 Feb 2011, 09:46
217) A certain junior class has 1,000 students and a certain senior class has 800 students.among these students, there are 60 sibling 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) 3/40,0000 b) 1/3600 c) 9/2000 d) 1/60 e) 1/15 Probability to select one senior student who is sibling is 60/800 Probability to select one junior student who is sibling is 60/1000 As both the events are independent and should happen we ill multiply the two probabilities 60/800 * 60/1000 = 9/2000 Pls tell me the error in my solution
_________________
The proof of understanding is the ability to explain it.



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: Probability to select sibling [#permalink]
Show Tags
19 Feb 2011, 09:55
Merging similar topics. Also discussed here: junior58914.html?hilit=certain%20junior%20class#p778756GMATD11 wrote: 217) A certain junior class has 1,000 students and a certain senior class has 800 students.among these students, there are 60 sibling 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) 3/40,0000 b) 1/3600 c) 9/2000 d) 1/60 e) 1/15
Probability to select one senior student who is sibling is 60/800 Probability to select one junior student who is sibling is 60/1000
As both the events are independent and should happen we ill multiply the two probabilities 60/800 * 60/1000 = 9/2000
Pls tell me the error in my solution Please ask if anything remains unclear.
_________________
New to the Math Forum? Please read this: 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? Extrahard Quant Tests with Brilliant Analytics



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2010

Re: Probability to select sibling [#permalink]
Show Tags
19 Feb 2011, 10:01
GMATD11 wrote: 217) A certain junior class has 1,000 students and a certain senior class has 800 students.among these students, there are 60 sibling 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) 3/40,0000 b) 1/3600 c) 9/2000 d) 1/60 e) 1/15
Probability to select one senior student who is sibling is 60/800 Probability to select one junior student who is sibling is 60/1000
As both the events are independent and should happen we ill multiply the two probabilities 60/800 * 60/1000 = 9/2000
Pls tell me the error in my solution If probability of selecting one senior student is 60/800 Probability of selecting the matching pair from the junior students becomes 1/1000 Think it like this; You have successfully chosen 1 sibling of sibling pairs from the senior students. Now; when you start choosing from the juniors; you just have 1 favorable outcome. Because; out of these 1000 students, there is only 1, just ONE student who is the paired sibling of the student you earlier chose from the senior students. Got it? So; the total probability becomes = 60/800*1/1000 = 3/40000. Ans: "A" I believe there was a similar post yesterday. Also; this particular question is also discussed elsewhere. Guess this post is going to be short lived.
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Senior Manager
Joined: 10 Nov 2010
Posts: 262
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19 GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)

Re: Probablility [#permalink]
Show Tags
19 Feb 2011, 20:45
Thanks Bunuel and Fluke its clear now
_________________
The proof of understanding is the ability to explain it.



Manager
Joined: 30 Jan 2010
Posts: 68

Re: Probablility [#permalink]
Show Tags
28 Feb 2011, 08:07
i had also missed the "pairs" word so I had 30 pairs and 60 siblings... thanks for the explanations bunuel



Intern
Joined: 24 Feb 2012
Posts: 33

60/1000 * 1/800 = 6/80000 = 3/40000. A.



Intern
Joined: 27 Mar 2012
Posts: 17

A certain junior class has 1000 students and a certain senio [#permalink]
Show Tags
13 Apr 2012, 02:32
A certain junior class has 1000 students and a certain senior class has 800 students.Among these students there are 60 sibling 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) 3/40,000 (B) 1/3600 (C) 9/2000 (D) 1/60 (E) 1/15
OA is A. Can someone provide the solution?



VP
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1254
GRE 1: 1540 Q800 V740

Re: A certain junior class has 1000 students and a certain senio [#permalink]
Show Tags
13 Apr 2012, 05:14
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 ReviewBest MBA Interview PreparationExclusive GMAT coaching
Get a FREE Detailed MBA Profile Evaluation  Call us now +91 98998 31738



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: A certain junior class has 1000 students and a certain senio [#permalink]
Show Tags
13 Apr 2012, 11:01



Senior Manager
Joined: 30 Jun 2011
Posts: 266

Re: A certain junior class has 1000 students and a certain [#permalink]
Show Tags
17 Apr 2012, 07:22
Bunuel, Sometimes i get confused if i have to take the opposite order into consideration. Like in this problem
prob(1st senior then junior) + prob(1st junior then senior) BUT you found only one of these. how to decide when you have to take both of the case



Senior Manager
Joined: 30 Jun 2011
Posts: 266

Re: A certain junior class has 1000 students and a certain [#permalink]
Show Tags
17 Apr 2012, 23:19
Anyone please clear my doubt. I have a similar ques A bag has 6 red marbles and 4 marbles. What are the chances of pulling out a red and blue marble. Method 1: # of ways of picking 1 red and 1 blue marble = (6c1)(4c1) = 6 x 4 = 24; # of ways of picking 2 marbles in general = 10c2 = 45. therefore, probability = 24/45 Method 2: Total prob = prob ( R then B) + P (B then R) 6 ways for red and 4 ways for blue = 24 total ways = 10*9 Prob ( R then B) = 24/90
ly Prob ( B then R) = 24/90 Therfore total = 24/45



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16024

Re: A certain junior class has 1000 students and a certain [#permalink]
Show Tags
07 Jul 2014, 21:17
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
Status: A mind once opened never loses..!
Joined: 05 Mar 2015
Posts: 222
Location: India
MISSION : 800
WE: Design (Manufacturing)

Re: A certain junior class has 1000 students and a certain [#permalink]
Show Tags
10 May 2015, 23:30
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 <



eGMAT Representative
Joined: 04 Jan 2015
Posts: 726

Re: A certain junior class has 1000 students and a certain [#permalink]
Show Tags
11 May 2015, 00:25
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
_________________
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



Manager
Status: A mind once opened never loses..!
Joined: 05 Mar 2015
Posts: 222
Location: India
MISSION : 800
WE: Design (Manufacturing)

Re: A certain junior class has 1000 students and a certain [#permalink]
Show Tags
11 May 2015, 00:30
EgmatQuantExpert wrote: 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 Hi Harsh I think my doubt is clear now in both the cases the pair will be the same thnx 4 the reply
_________________
Thank you
+KUDOS
> I CAN, I WILL <



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16024

Re: A certain junior class has 1000 students and a certain [#permalink]
Show Tags
26 Jun 2016, 11:05
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




Re: A certain junior class has 1000 students and a certain
[#permalink]
26 Jun 2016, 11:05







