I have a problem:
There is a bag of 75 balls with 15 Red and rest Blue.
I pick 4 balls at the start of every turn.If I get to pick at least 1 red ball, I fill 1 cell with X.
If I get 3 red balls and 1 blue ball, I fill 3 X. If I get no red balls at all, I fill O. This means, if I pick at least 1 red ball, I fill as many X's as I pick blue balls. If I pick no red balls, I fill just 1 O.
All I do after this is fill Tic Tac Toe in sequential of 1 to 9 (left to right) cells at every turn.
After every turn, I put back the balls and start fresh.
If I happen to make a pattern of 3 Xs then, I win the board.
If I happen to make a pattern of 3 Os then, I lose the board.
What is the probability of me winning board ?
How does the probability change if I pick 3 balls at a time instead of 4 balls ?
More than solution, I'm looking for approach to this problem.
Can some one please help ?