Sock Drawer

Question

Suppose I have 18 socks in a drawer, 6 brown and 12 green.  Because of what I am wearing, I want a pair of brown socks.  Suppose I draw 4 socks at random from the drawer, what is the probability of a pair of brown socks?

 

What methods do you suggest?

Answer 1

Jim.

This statement of the problem is confusing; is the goal the drawing of at least 2 brown socks, or of only 2 brown socks? It really matters; the former lets you draw, for example, 2 brown socks, then 2 of any color, and then multiply for the combinations, whereas the latter requires you to draw 2 brown socks, then two green socks, then multiply for the combination.

So the former problem would be:

6/18 * 5/17 * 16/16 * 16/16 * 6 ways[4!/(2!*2!)] = 0.588

and the second would be:

6/18 * 5/17 * 12/16 * 11/15 * 6 ways ~= 0.324

Note: as far as methods go, in the spirit of "Math Curse" (Jan Scieszka), I put on any two socks, and tell people I'm color-blind (which I am).