OG - PS - #217

[gt2011]

Hey guys and Stacey

Thanks for the original post on OG #217 by slsu on Mon Sep 17, 2007 10:43 pm (copy and pasted below). However, I still don't understand "the second "winning event" looks at the probability that the student from the senior class (800 students) is the other member of the pair. This results in a P = 1/800." I thought the second winning event is 60/800 [b/c there are 60 pairs, or 120 people to start with].

Can someone explain this to me?

Thanks a lot!

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Question:
[Deleted because this question is from a banned source - see below.]

Answer:
(A)

I looked at this problem as having 2 winning scenarios:

(1) 1 Junior, 1 Senior
(2) 1 Senior, 1 Junior

In (1), the "winning scenario" the first "winning event" looks at the probability that the student from the junior class (1,000 students) is a member of a sibling pair (60 pairs). This results in a P = 60/1,000. Then, the second "winning event" looks at the probability that the student from the senior class (800 students) is the other member of the pair. This results in a P = 1/800. The probability of this "winning scenario" is (60/1,000)*(1/800) = 3/40,000.

My question is how come we don't also look at the 2nd winning scenario (2), since a senior could be picked first, then a junior? Then, the probability of either event chain - (1) or (2) occurring would be the sum of these individual probabilities?

[JK]

Its the same either way you choose junior or senior first. Since the events both need to occur together, you multiple.

[StaceyKoprince]

Please read (and follow!) the forum guidelines before posting. OG is a banned source; it is illegal to post OG questions anywhere on the web. We still have the archive of questions up from before the ban, as a convenience to everyone, but we can't post these questions now. If you are in one of our classes, please ask OG questions during office hours or before/after class.

A quick response here though: JK answers one of your questions (why we multiple instead of adding). Here's the other thing: the reason the second event is just 1 instead of 60 is that you are trying to match two actual siblings, not one person who has a sibling with another person who has a sibling (but they're not each others' siblings).

Once you pick one person, say, Susie, from the junior class, there's only one person you can pick from the senior class to fulfill the requirement: her brother Johnny. (Or vice versa, if you start with the senior class.) If you picked any one of the other 59 seniors with siblings in the junior class, those people would not be Susie's sibling.

If you have additional questions on this one, talk to your instructor!