garry123 wrote:Why the following reasoning is wrong:
total number of students = 800+500 = 1300
total of number of sibling pairs = 30
= total number of students having the tag of sibling = 2*30 = 60
thus probability = 60/1300 = 6/130
The question in the original post is actually an almost word-for-word copy of a question in the Official Guide (with a few details changed). You can see the OG version here:
www.beatthegmat.com/a-sibling-pair-t34354.html
I'm curious where the question is from. I've been seeing a lot of these nearly exact replicas of OG problems posted in this forum, and if they're being sold by a company as 'original problems', that would seem like false advertising to me; a problem is not 'original' (or particularly helpful to test takers) if it's copied from the OG with a few numbers changed. In any case, whoever 'copied' this question did not do a good job of it, since he or she changed an important word:
YellowSapphire wrote:A certain business school has 500 students, and the law school at the same university has 800 students. Among these students, there are 30 sibling pairs consisting of 1 business student and 1 law student. If 1 student is selected at random from both schools, what is the probability that a sibling pair is selected?
In the OG version, the word 'both' (highlighted above) actually reads 'each'. So the OG question makes clear that you are choosing two students, one from each class. In the imitation question above, the word 'both' is imprecise; one could easily interpret the phrase "if one student is selected... from both schools" to mean that we will select a single student from the group of all students attending either school.
That's the interpretation garry123 made in his post above, and it's a reasonable interpretation from the wording of the question. So garry has answered the question: if you pick one student from the 1300 students at either school, what is the probability that he or she belongs to a sibling pair? While the wording of the question does not make this clear, the intended question here is 'if you pick one student from the law school and one from the business school, what's the probability they are siblings?'
