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A certain junior class has 1000 students and a certain

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A certain junior class has 1000 students and a certain [#permalink] New post 13 Aug 2010, 02:15
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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..
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Feb 2012, 21:48, edited 1 time in total.
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Re: Probablility [#permalink] New post 13 Aug 2010, 02:33
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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.
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Re: Probablility [#permalink] New post 13 Aug 2010, 06:57
Ah... I missed the "sibling pair" word!! And my explanation was also wrong! :-( Thanks buddy!
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Probability to select sibling [#permalink] New post 19 Feb 2011, 08:46
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
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Re: Probability to select sibling [#permalink] New post 19 Feb 2011, 08:55
Expert's post
Merging similar topics.

Also discussed here: junior-58914.html?hilit=certain%20junior%20class#p778756

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


Please ask if anything remains unclear.
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Re: Probability to select sibling [#permalink] New post 19 Feb 2011, 09:01
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.
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Re: Probablility [#permalink] New post 19 Feb 2011, 19:45
Thanks Bunuel and Fluke its clear now
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Re: Probablility [#permalink] New post 28 Feb 2011, 07:07
i had also missed the "pairs" word :(
so I had 30 pairs and 60 siblings...

thanks for the explanations bunuel
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new [#permalink] New post 29 Feb 2012, 10:16
60/1000 * 1/800
= 6/80000
= 3/40000. A.
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A certain junior class has 1000 students and a certain senio [#permalink] New post 13 Apr 2012, 01:32
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?
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Re: A certain junior class has 1000 students and a certain senio [#permalink] 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).
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Re: A certain junior class has 1000 students and a certain senio [#permalink] New post 13 Apr 2012, 10:01
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sugu86 wrote:
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?


Merging similar topics. Please ask if anything remains unclear.
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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

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Re: A certain junior class has 1000 students and a certain [#permalink] New post 17 Apr 2012, 06:22
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
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Re: A certain junior class has 1000 students and a certain [#permalink] New post 17 Apr 2012, 22:19
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
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Re: A certain junior class has 1000 students and a certain [#permalink] New post 07 Jul 2014, 20:17
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Re: A certain junior class has 1000 students and a certain   [#permalink] 07 Jul 2014, 20:17
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