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 ?

  • $\begingroup$ IMHO, this question is better suited for Math SE. $\endgroup$ – Glorfindel Jan 26 '17 at 9:09
  • $\begingroup$ This seems like a basic math problem. Not a puzzle. Also looks like homework, which we don't usually help. $\endgroup$ – stack reader Jan 26 '17 at 9:09
  • $\begingroup$ Nope. Its not homework. Trying to solve a real world specific case problem through this solution. $\endgroup$ – MogambO Jan 26 '17 at 9:12
  • $\begingroup$ Please edit for clarity, esp. fourth paragraph. It currently contradicts itself. $\endgroup$ – Wen1now Jan 26 '17 at 9:55
  • $\begingroup$ The probability is pretty high if you're putting in the Os and Xs $\endgroup$ – Alfie Goodacre Jan 26 '17 at 12:52