Probability of A winning the game

[TomJerry]

Suppose A and B play over and over , independently a game which each time results in either a win for A , a win for B or draw (meaning no decision) with probabilities P(A), P(B) and P(D). Suppose they keep playing until the first game that does not result in a draw , and call the winner of that game the overall winner. Compute
i) P(A wins at game n)
ii) P(a wins)

 

[ych22]

P(A,n) = P(draw in first n-1 games) * P( A wins in nth game | draw in first n-1 games)

P(A wins) = P(A wins first game) + P(A wins second game) + ...

This seems like it belongs to the homework guidance forum though

 

[Bacle]

I think laying out clearly the sample space should take you around 90% towards
the answer.