# Chess - PMF

1. Oct 21, 2007

### janela

1. The problem statement, all variables and given/known data

Two world champion chess players play a sudden-death chess match where the first player to win a game wins the match. Each game is won by the first player with probability p and by the 2nd player with probability q and is a tie with probability (1-p-q).

a) what is the probability that the first player wins the match?
b) what is the Probability Mass Function, the mean, and the variance of the duration (number of games) of the match?

2. Relevant equations

3. The attempt at a solution

a) I think that this is a geometric random variable, seeing how many games (k) are needed for Wallace to win.
Px(k)= (1-p)^(k-1) p
yet I am not sure how to take into account that Wallace win FIRST, the games that come before him winning can only be ties.
does the equation of wallace NOT winning help at all?
= 1 - [ (1-q)^(k-1) q]

2. Oct 22, 2007

### CompuChip

- What is the chance that there is a tie?
- Then what is the chance that there are k - 1 ties in a row?
- What is the chance that there are k - 1 ties in a row and Wallace wins the kth game?