Socks

-Removed-

Hmm, seeing as its not about probability, how would you work out the chance of having a match after 4 socks?

Originally posted by forkedknight
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.

Oops, sorry, forgot the initial conditions entirely!

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

Originally posted by iamatiger
Hmm, seeing as its not about probability, how would you work out the chance of having a match after 4 socks?

8 white, 6 black, 4 brown, 2 tan

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%