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A certain junior class has 1000 students and a certain [#permalink]
13 Aug 2010, 02:15

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Difficulty:

25% (low)

Question Stats:

69% (01:42) correct
30% (00:58) wrong based on 39 sessions

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.

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}.

Probability to select sibling [#permalink]
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
_________________

The proof of understanding is the ability to explain it.

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.
_________________

Re: Probability to select sibling [#permalink]
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.
_________________

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

Re: A certain junior class has 1000 students and a certain senio [#permalink]
13 Apr 2012, 10:01

Expert's post

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 ?

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

gmatclubot

Re: A certain junior class has 1000 students and a certain
[#permalink]
17 Apr 2012, 22:19