Seven sportsmen (named A,B,C,D,E,F and G) buy 7 hats choosing randomly out of 4 available colors (say G,R,W and Y).
What is the probability that all the colors were chosen?

Each sportsmen has a 3/4 chance of excluding a given color.  Starting with the color Y,there is a .133 (3/4 ^7) chance that none of the sportsmen will pick it.  But there are 4 possible colors which may be excluded by all 7 sportsmen.  So multiply .133 * 4 = .5339.  That is probability that any single color will be excluded by all 7 sportsmen.  So the probability that this won't happen (and all colors will be chosen) is 1 - .5339, or .4661

Posted by John zadeh on 2010-04-27 19:40:42