Help with some probably questions please? :p

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nickh

Full Member
7+ Year Member
Hey guys, so I was tutoring a student, but got stuck on this question:

A drawer contains 5 pairs of green socks, 3 pairs of black socks, and 4 pairs of red socks. All of the pairs are together, meaning that there are not 24 randomly distributed socks, but 12 pairs. You reach into the drawer and pull out 3 pairs of socks without putting any back.
  1. What is the probability that you get 2 pairs of green socks? Leave your answer as a fraction in lowest terms.
  2. What is the expected number of pairs of green socks?
It's not directly DAT related, but could be worthwhile knowing? 😛

Thanks so much in advance!!
 
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i find this more fun than i should.
 

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This is a tough one...Not exactly sure if this is right but here goes
Assuming that you pick out one pair of the same color at a time...
1. 7 (5C2/12C3) = 7 (10/220) = 70/220
Logic: There are 12 choose 3 ways to choose 3 pairs out of 12 pairs. = Total outcome
There are 5 choose 2 ways to choose 2 pairs of green out of 5 pairs.
--> Each case also has 7 different cases because you still have 7 other pairs left (3 black + 4 red pairs) So multiply by 7.
2. 5/12 x 3 = 1.25 pair?
 
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