If I put nine pieces of paper, with a digit from 19 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 tictactoe?
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 20040730 13:11:40 