OG Question 217 -> Please explain

[jymloke]

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 ?

[orel]

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

[jymloke]

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

[Abdulla]

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

[hrishikesh05]

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

[Stuart@KaplanGMAT]

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

[jackcrystal]

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

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