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

Question

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

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

Bunuel · Accepted Answer

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

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

What is the probability of choosing the  PAIR  of the chosen sibling in the senior class? Since there is only  one  corresponding sibling in the senior class, the probability is  \frac{1}{800}  (since there are 800 students in the senior class).

Therefore, the probability that the two 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:

Total number of outcomes:

In how many ways can we choose 1 person from 1000 in the junior class?
 C^1_{1000} = 1000 .

In how many ways can we choose 1 person from 800 in the senior class?
 C^1_{800} = 800 .

So, the total number of ways to choose 1 person from 1000 and 1 person from 800 is  1000 * 800 , which gives the total number of outcomes.

Favorable outcomes:

In how many ways can we choose 1 sibling from the 60 in the junior class?
 C^1_{60} = 60 .

The pair of the one chosen in the senior class:  C^1_1 = 1 .

So, the total number of favorable outcomes is  60 * 1 = 60 .

Probability:

The probability of selecting a sibling pair is:

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

Answer: A.

Now, let’s consider another example:

There are 1000 students in the junior class and 800 students in the senior class. Among these students, there are 60 sibling groups, with each group consisting of 2 juniors and 2 seniors (a total of 240 students: 2 in the junior class and 2 in the senior class for each sibling group). 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?

Probability of choosing a sibling from the junior class: 
 
 \frac{120}{1000}  (since there are 120 siblings in total in the junior class).

Probability of choosing the sibling's pair from the senior class: 
 
 \frac{2}{800}  (since there are 2 corresponding siblings in the senior class).

Final probability: 
 
 \frac{120}{1000} * \frac{2}{800} = \frac{3}{10000} .

Another approach:

Total number of outcomes:  1000 * 800 .

Favorable outcomes:  120 * 2 = 240 .

Probability:  \frac{240}{1000 * 800} = \frac{3}{10000} .

eschn3am · Answer

https://gmatclub.com/cgi-bin/mimetex.cgi?formdata=%5Cfrac%7B60*1%7D%7B1000*800%7D+%3D+%5Cfrac%7B60%7D%7B800000%7D%3D%5Cfrac%7B3%7D%7B40000%7D

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  https://gmatclub.com/cgi-bin/mimetex.cgi?formdata=%5Cfrac%7B60%7D%7B1000%7D  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  https://gmatclub.com/cgi-bin/mimetex.cgi?formdata=%5Cfrac%7B1%7D%7B800%7D  chance of choosing the sibling.

Multiply the two equations together and simplify...and there's your answer.

Sleepless · Answer

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

Sleepless · Answer

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?

eschn3am · Answer

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.

DFG5150 · Answer

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

Bunuel · Answer

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jeeteshsingh · Answer

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

jananijayakumar · Answer

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

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..

Bunuel · Answer

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.

diptich12 · Answer

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?

Bunuel · Answer

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.

adg142000 · Answer

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

Bunuel · Answer

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.

KarishmaB · Answer

Check out this post: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/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.

iamdp · Answer

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} .

EgmatQuantExpert · Answer

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

SVaidyaraman · Answer

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

JeffTargetTestPrep · Answer

The probability of selecting any one sibling from the 60 sibling pairs in the junior class is 60/1000. Once that person is selected, the probability of selecting his or her sibling from the senior class is 1/800; thus, the probability of a selecting a sibling pair is:

60/1000 x 1/800 = 3/50 x 1/800 = 3/40000

Alternatively, the probability of selecting any one sibling from the 60 sibling pairs in the senior class is 60/800. Once that person is selected, the probability of selecting his or her sibling from the junior class is 1/1000; thus, the probability of a selecting a sibling pair is:
 
60/800 x 1/1000 = 3/40 x 1/1000 = 3/40000

Answer: A

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