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OG #217 question

by jamesk486 » Thu Apr 19, 2007 6:42 am

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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 a student is to be selected at random from each class, what is the probabilty that the 2 students selected will be a sibling pair?
A. 30/40,000
B. 1/3600
C. 9/2000
D. 1/60
E. 1/15

why is it (60/1000)(1/800)?
60/1000= a junior who is a member of a sibling pair, but shouldn't it be 30? Bc 30 should be juniors and 30 should be seniors?
And then why not (60/800) or (30/800)?
i solved it like (30/1000)*(30/800)
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by Cybermusings » Thu Apr 19, 2007 8:13 am
Ans Choice A here is 3/40,000 and not 30/40,000

Probability that out of 1000 junior students, we pick from a student from a sibling pair = 30/1000

Probability that out of the 800 senior students we pick a student who is the other half of the same sibling pair =1/800

So 60/1000 * 1/800 = 6/100*1/800 = 3/40,000 = 3/40,000

You have to keep in mind that the second selection is made after the first selection is already through and hence we select 1/800 and not 60/800
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by Scott@TargetTestPrep » Mon Nov 12, 2018 7:26 am
jamesk486 wrote: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 a student is to be selected at random from each class, what is the probabilty that the 2 students selected will be a sibling pair?
A. 30/40,000
B. 1/3600
C. 9/2000
D. 1/60
E. 1/15
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

We would obtain the same answer if we made our first selection from the senior class: 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 also:

60/800 x 1/1000 = 3/40 x 1/1000 = 3/40000

Answer: 3/40000

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by Brent@GMATPrepNow » Mon Nov 12, 2018 8:36 am
jamesk486 wrote: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 a student is to be selected at random from each class, what is the probabilty that the 2 students selected will be a sibling pair?
A. 30/40,000
B. 1/3600
C. 9/2000
D. 1/60
E. 1/15
P(selecting a sibling pair) = P(select a junior with a sibling AND select the senior who is that junior's sibling)
= P(select a junior with a sibling) x P(select the senior who is that junior's sibling[/u])
= 60/1000 x 1/800
= 60/800,000
= 3/40,000
= A

Note: P(select a junior with a sibling) = 60/1000, because 60 of the 1000 juniors have a sibling who is a senior.
P(select a senior who is that junior's sibling) = 1/800, because there are 800 senior's and only 1 of them is the sibling of the selected junior.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by fskilnik@GMATH » Mon Nov 12, 2018 1:21 pm
jamesk486 wrote: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 a student is to be selected at random from each class, what is the probabilty 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
$$\left( J \right)\,\,{\text{Junior}}\,\,:\,\,\,1000\,\,{\text{students}}\,\,,\,\,\,{J_1}\,,\,{J_2},\,\, \ldots \,\,,\,\,{J_{60}}\,\,{\text{among}}\,\,{\text{them}}\,\,\,\left( {{\text{the}}\,\,{\text{ones}}\,\,{\text{with}}\,\,{\text{senior}}\,\,{\text{siblings}}} \right)$$
$$\left( S \right)\,\,{\text{Senior}}\,\,:\,\,\,800\,\,{\text{students}}\,\,,\,\,\,{S_1}\,,\,{S_2},\,\, \ldots \,\,,\,\,{S_{60}}\,\,{\text{among}}\,\,{\text{them}}\,\,\,\left( {{\text{the}}\,\,{\text{ones}}\,\,{\text{with}}\,\,{\text{junior}}\,\,{\text{siblings}}} \right)$$
$$\left( {{J_1}\,,\,{S_1}} \right)\,\,;\,\,\left( {{J_2}\,,\,{S_2}} \right)\,\,;\,\, \ldots \,\,;\,\,\left( {{J_{60}}\,,\,{S_{60}}} \right)\,\,\,:\,\,\,{\text{pairs}}\,\,{\text{of}}\,\,{\text{siblings}}\,$$
$$? = P\left( {{\text{pair}}\,{\text{of}}\,{\text{siblings}}\,,\,\,{\text{in}}\,{\text{one}}\,J\,{\text{and}}\,{\text{one}}\,S\,{\text{extraction}}} \right)$$
$${\text{Total}}\,\,:\,\,\,1000 \cdot 800\,\,\,{\text{equiprobable}}\,\,\,{\text{selections}}\,\,\,\left[ {\left( {{J_m},{S_n}} \right)\,\,,\,\,\,{\text{where}}\,\,1 \leqslant m \leqslant 1000\,\,{\text{and}}\,\,\,1 \leqslant n \leqslant 800} \right]$$
$${\text{Favorable}}\,\,:\,\,60\,\,\,\,\,\left[ {\left( {{J_k},{S_k}} \right)\,\,,\,\,\,{\text{where}}\,\,1 \leqslant k \leqslant 60} \right]\,\,\,\,$$
$$? = \frac{{60}}{{1000 \cdot 800}} = \underleftrightarrow {\frac{{4 \cdot 15}}{{1000 \cdot 4 \cdot 200}}} = \frac{{4 \cdot 3 \cdot 5}}{{1000 \cdot 4 \cdot 5 \cdot 40}} = \frac{3}{{40 \cdot 1000}}$$


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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