Chess Match Question-Probability Mass Functions

Fischer and Spassky play a chess match in which the first player to win a game wins the match. After 5 successive draws, the match is declared drawn. Each game is won by Fischer with probability 0.31, is won by Spassky with probability 0.23, and is a draw with probability 0.46, independently of the previous games. (Please use four digits after the decimal in your answers below.)

- What is the probability that Fischer wins the match?
- Let X be the number of games played in the match. Indicate the PMF of X by filling the boxes below:

P(X = 1) = - P(X = 2) =
- P(X = 3) =
- P(X = 4) =
- P(X = 5) =