If I put nine pieces of paper, with a digit from 1-9 written on each one, into a hat, and pull 3 out without replacement, what is the likelihood that I will select three numbers that result in a winning tic-tac-toe?

 1 | 2 | 3 
---+---+---
 4 | 5 | 6 
---+---+---
 7 | 8 | 9 

(In reply to Answer by Old Original Oskar!)

If the first number selected is a corner
the next number can be any 6 from 8, the final number can only be 1 from the remaining 7.

If the first number selected is a side
the next number can be any 4 from 8, the final number can only be 1 from 7.

If the middle number is selected first
the second number can be any. the final number can only be 1 from 7

Corner (4/9)x(6/8)x(1/7)=0.04761895.
Side (4/9)x(4/8)x(1/7)=0.03174996.
Middle (1/9)x(8/8)x(1/7)=0.01587301.

Add all the above probabilities together = 0.09524192

9.524192%

Posted by Juggler on 2004-07-30 13:11:40