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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]

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12 Dec 2009, 09:37
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Feb 2012, 22:50, edited 1 time in total.
Edited the question and added the OA

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12 Dec 2009, 09:50
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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

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: $$\frac{60}{1000}*\frac{1}{800}=\frac{3}{40000}$$

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 $$C^1_{60}*C^1_1=60$$

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

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12 Dec 2009, 10:20
Bunuel wrote:
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? 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 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: 60/1000*1/800=3/40000

This problem can be solved in 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.

Let’s count favorable outcomes: 1 from 60=60C1=60
The pair of the one chosen=1C1=1
So total favorable outcomes=60C1*1C1=60

Probability=Favorable outcomes/Total # of outcomes=60/(1000*800)=3/40000

thnks Bunnel...i have followed some of your posts and your explanations are awesome.
can u please tell me how to improve probability

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12 Dec 2009, 15:32
gurpreet07 wrote:
thnks Bunnel...i have followed some of your posts and your explanations are awesome.
can u please tell me how to improve probability

Probability will improve based on counting techniques. First get your Permutations and Combinations perfect. If you can understand the scenarios based on which counting occurs, probability is just a division of required sample of outcomes of the total possible outcomes. Discrete probability and it's terms like equally likely, mutually independent etc can be understood better if you understand simple probability, the ability to just simply divide the appropriate outcomes.
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14 Dec 2009, 08:59
Thanks for showing to different solutions. I feel like using the probability/combination formula for this problem would be time consuming. I found it easier to use the first one. However, using the first way isnt as consistent of a method for me to use for other problems.

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15 Jun 2010, 06:09
I am not sure if my explanation is accurate, but here's my take on it:

Number of juniors = 1000
Number of seniors = 800
Number of sibling pairs = 60

The problem is such that it doesn't matter if we pick a junior first or a senior first, but just for clarity, I've outlined how I would solve both the cases. So, let us approach this one at a time:

Case 1: We pick a junior first

Chances of us selecting a junior who has a sibling is given by : P(A) = $$\frac{60}{1000}$$

Now, for the second student we select the chances of the student being the sibling of the first student we selected is: $$P(B) = \frac{1}{800}$$

So the total probability of selecting a sibling pair would be $$P(A)*P(B)$$

This comes down to: $$\frac{60}{1000} * \frac{1}{800} = \frac{3}{40000}$$

Case 2: We pick a senior first

Note that if you were to switch the order around, the answer remains the same. That is, if you were to pick a senior first, then the chances of selecting one who has a sibling is given by: $$P(A) = \frac{60}{800}$$

Now, probability of picking the corresponding senior: $$P(B) = \frac{1}{1000}$$

So, overall probability = $$P(A) * P(B) = \frac{3}{40000}$$

Hope this helps!

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A certain junior class has 1000 students and a certain [#permalink]

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13 Aug 2010, 03:15
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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..

Last edited by Bunuel on 14 Feb 2012, 22:48, edited 1 time in total.
Edited the question

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A certain junior class has 1000 students and a certain [#permalink]

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13 Aug 2010, 03:33
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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.
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13 Aug 2010, 07:57
Ah... I missed the "sibling pair" word!! And my explanation was also wrong! Thanks buddy!

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Re: Probability to select sibling [#permalink]

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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.
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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

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Re: A certain junior class has 1000 students and a certain senio [#permalink]

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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).
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Re: A certain junior class has 1000 students and a certain [#permalink]

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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

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Re: A certain junior class has 1000 students and a certain [#permalink]

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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

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Re: A certain junior class has 1000 students and a certain [#permalink]

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29 Dec 2013, 17:22
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

Good one.

Let's see

Pick 60/1000 first

Then we can only pick 1 other pair from the 800

So total will be 60 / 800 *1000

Simplify and you get 3/40000

Hope it helps

Cheers!
J

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Re: A certain junior class has 1000 students and a certain [#permalink]

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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: $$\frac{60}{1000}*\frac{1}{800}=\frac{3}{40000}$$

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 $$C^1_{60}*C^1_1=60$$

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

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>>

$$Probability=\frac{60}{1000} * \frac{1}{800} OR \frac{60}{800} * \frac{1}{1000} = \frac{3}{20000}$$.
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Re: A certain junior class has 1000 students and a certain [#permalink]

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11 May 2015, 00:25
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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: $$\frac{60}{1000}*\frac{1}{800}=\frac{3}{40000}$$

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 $$C^1_{60}*C^1_1=60$$

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

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
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Re: A certain junior class has 1000 students and a certain [#permalink]

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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: $$\frac{60}{1000}*\frac{1}{800}=\frac{3}{40000}$$

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 $$C^1_{60}*C^1_1=60$$

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

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
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Re: A certain junior class has 1000 students and a certain [#permalink]

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31 May 2017, 22:46
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
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