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All the colors in (Posted on 2010-04-26) Difficulty: 3 of 5
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?

See The Solution Submitted by Ady TZIDON    
Rating: 5.0000 (1 votes)

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Solution | Comment 4 of 21 |
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 19:30:10
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