OG Question 217 -> Please explain

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jymloke: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Sun Nov 09, 2008 10:23 pm; Location: Melbourne; Thanked: 1 times

by jymloke » Fri Nov 21, 2008 10:02 pm

Q. 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 selected at random from each class, what is the probability that the 2 students selected will be a sibling pair ??

Answer: 3 / 40,000

My answer: 9 / 2,000

My reasoning: Since there are 60 sibling pairs, hence there are 120 students total in the pair, 60 of which are senior, and the rest junior. Probability of selecting a student from this pair in junior is (60/1000) and probability for selecting senior is (60/800). Multiply the two, and you arrive 9/2000

But the answer is 3/40000.

Do you guys see where my flaw in reasoning is at ?

THANKS

My GMAT is in less than 1.5 week

So far, got scores of 680 and 690 in the GMATPrep, but have heaps of errors while doing the test.... Anyone experiences this ?

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Source: Beat The GMAT — Problem Solving | Fri Nov 21, 2008 10:02 pm

orel: Master | Next Rank: 500 Posts; Posts: 247; Joined: Sun Jul 27, 2008 1:39 am; Thanked: 2 times; GMAT Score:660

Re: OG Question 217 -> Please explain

by orel » Sat Nov 22, 2008 1:18 am

jymloke wrote:Q. 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 selected at random from each class, what is the probability that the 2 students selected will be a sibling pair ??

Answer: 3 / 40,000

The probability that the one of 60 siblings will be chosen among 1000 juniors is : 60/1000
the probability that another one of 60 will be chosen among 800 seniors is 60/800
and the probability that the ones chosen is a pair of siblings is 1/60
When multiplied we get: 60/1000*60/800*1/60=3/40000

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jymloke: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Sun Nov 09, 2008 10:23 pm; Location: Melbourne; Thanked: 1 times

by jymloke » Sat Nov 22, 2008 3:31 pm

Ahh I missed the 1/60 .... Damn. Thanks !!!

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Abdulla: Master | Next Rank: 500 Posts; Posts: 328; Joined: Thu Aug 07, 2008 5:25 pm; Location: Philadelphia; Thanked: 4 times; GMAT Score:550

by Abdulla » Sat Nov 22, 2008 8:02 pm

Try this ..
60/1000 * 1/800 = 3/ 40000

Abdulla

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hrishikesh05: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Sat Jul 05, 2008 11:07 pm; Thanked: 2 times

by hrishikesh05 » Sat Nov 22, 2008 10:25 pm

The questions asks for the probability of a choosing a sibling pair (brothers / sisters from the same family) and not any siblings. Having cleared that lets see how we can solve the question

60 pairs of siblings that means 60 siblings in each class i.e. senior and junior

Probability of choosing a sibling - first class 60/1000
Probability of the sibling of the child chosen in the first class from the second class - 1/800 (since there will be only one sibling for the first chosen)

Total Probability = 60/1000 * 1 /800 = 3/40000

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Sat Nov 22, 2008 10:34 pm

hrishikesh05 wrote:The questions asks for the probability of a choosing a sibling pair (brothers / sisters from the same family) and not any siblings. Having cleared that lets see how we can solve the question

60 pairs of siblings that means 60 siblings in each class i.e. senior and junior

Probability of choosing a sibling - first class 60/1000
Probability of the sibling of the child chosen in the first class from the second class - 1/800 (since there will be only one sibling for the first chosen)

Total Probability = 60/1000 * 1 /800 = 3/40000

Great solution!

Note that we could have started with either class and reached the same answer.

If we had started with:

Prob choosing a sibling from Sr class: 60/800

then we'd have:

Prob of choosing a match from jr class: 1/1000

60/800 * 1/1000 = 60/800000 = 6/80000 = 3/40000

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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jackcrystal: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Mon Aug 04, 2008 2:04 pm; Thanked: 1 times

by jackcrystal » Sun Nov 23, 2008 8:14 am

all possible pairs = 800*1000
but we have only 60 pairs that are siblings

Therefore, probability = 60 / (800 * 1000) = 3/40000

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