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22 Mar 10
Originally posted by forkedknightOops, sorry, forgot the initial conditions entirely!
Your math makes it seem like there are infinitely many socks in the drawer and they are evenly distributed between the 4 different color.
The problem does not reflect that.
There could be a million black socks, 19 red socks, 2 blue socks, and 1 green sock and the answer would still be 5.
first sock = colour a.
chance of second sock being colour a = (n_a - 1)/(n_socks - 1)
if not, second sock is colour b
chance of third sock being colour a or b = (n_a + n_b - 2)/(n_socks - 2)
if not, third sock is colour c
chance of fourth sock being a or b or c = (n+a + n_b + n_c - 3)/(n_socks - 3)
if not, fourth sock is colour d
chance of fifth sock being a or b or c or d = (n_a + n_b + n_c + n_d - 4)/(n_socks - 4)
seeing as
n_socks = n_a + n_b + n_c + n_d
the fifth sock chance = 1
24 Mar 10
2 edits
Originally posted by iamatiger8 white, 6 black, 4 brown, 2 tan
Hmm, seeing as its not about probability, how would you work out the chance of having a match after 4 socks?
20 socks in total, which means 20!/16!4! combinations of drawing 4 socks or 4,845
(assumption that each sock is distinct, order does not matter)
Of these, there are 8*6*4*2 combinations of all four color socks, or 384 ways, which means there are 4,461 ways to gets socks where you have at least 1 pair.
4,461 / 4,845 = 92.1% moreorless
Chance to match is as follows, according to my numbers
2 socks - 26.3%
3 socks - 64.9%
4 socks - 92.1%
5 socks - 100.0%