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 

Lets say you draw 1,3,7,9 first prob (4/9)
This gives you 3 possible 2 slip combinations that will allow you a line (3/56)

Lets say you draw 2,4,6,8, first prob (4/9)
this gives you 2 possible winning combinations that will give you a line (2/56)

Lets say you draw 5 prob (1/9)
this gives you 5 pairs that will give you a line
(5/56)

Using multiplicative and additive rule of disjoint probabilities we get 25/504

Posted by neshal on 2004-08-02 05:40:26