# Thread: Chess Match Question-Probability Mass Functions

1. ## 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.)

1. What is the probability that Fischer wins the match?
2. Let X be the number of games played in the match. Indicate the PMF of X by filling the boxes below:
P(X = 1) =
3. P(X = 2) =
4. P(X = 3) =
5. P(X = 4) =
6. P(X = 5) =

2. Hi

Fischer wins the match if :
- he wins the first game : probability = 0.31
- or if the first game is a draw (probability = 0.46) and he wins the second game (probability = 0.31) : probability = 0.46 x 0.31 = 0.1426
- etc ...

Review each case and make the sum to get the final probability

3. It didn't work out, when I try to submit it says wrong answer.

4. $\displaystyle P = 0.31 + 0.31\:\cdot\:0.46 + 0.31\:\cdot\:0.46^2 + 0.31\:\cdot\:0.46^3 + 0.31\:\cdot\:0.46^4 = 0.31\:\frac{1-0.46^5}{1-0.46} = 0.5623$

Do you find this value ?

5. I think I made a calculation mistake. Thank you!