Pairs of Socks (Posted on 2004-09-01)

	Submitted by SilverKnight
Rating: 3.0000 (1 votes)
Solution:	(Hide)
I brute forced it (via Excel), and found that 6 socks with only 1 white sock gives the correct ratio, but there's not a "white pair", which the problem requires. The next lowest number that will allow the necessary ratio is 55 socks with 45 of them being black (10 white socks). In which case, there are 1485 (55 x 54 / 2) ways of selecting pairs, 990 (45 * 44 / 2)of which are black pairs, and 45 (10 x 9 / 2)of which are white pairs. Therefore, the answer in question is 45/1485 which is ~0.0303030303 chance of getting a white pair. _____________________________________ The bonus requires us to have 540 socks, 441 of which are black. This will produce a likelihood of ~0.03333333 for a white pair.

	Subject	Author	Date
	An approximation	Steve Herman	2015-02-22 16:54:07
	answer	K Sengupta	2008-01-25 05:51:25
	re: nate	Nate	2004-09-09 13:12:05
	re(2): Solution (maybe) - Thanks	Nate	2004-09-09 13:10:33
	nate	Bon	2004-09-09 09:13:38
	re: Solution (maybe)	nikki	2004-09-03 15:54:59
	Solution (maybe)	Nate	2004-09-03 15:30:56
	Solution (maybe)	Nate	2004-09-03 15:30:09
	Solution (maybe)	Nate	2004-09-03 15:29:27
	reply to replies	Tristan	2004-09-02 18:42:30
	re: Solution to part 1	Federico Kereki	2004-09-01 20:57:30
	solution	Charlie	2004-09-01 20:03:59
	re(4): Solution to part 1 - almost, + Part 2	Juggler	2004-09-01 18:54:09
	re(3): Solution to part 1 - almost, + Part 2	Nosher	2004-09-01 18:52:36
	Solution to 1st part	Juggler	2004-09-01 18:28:13
	re(3): Solution to part 1 - almost, + Part 2	Thalamus	2004-09-01 18:20:03
	re(2): Solution to part 1 - almost, + Part 2	Nosher	2004-09-01 18:08:00
	re: Solution to part 1	Nosher	2004-09-01 18:01:52
	re: Solution to part 1 - almost, but not quite	Thalamus	2004-09-01 18:01:19
	Solution to part 1	Tristan	2004-09-01 17:45:48