# Math Help - Bayes Probability - Yankees and World Series

1. ## Bayes Probability - Yankees and World Series

The Yankees are playing the Dodgers in a world series. The Yankees win each
game with probability .6. What is the probability that the Yankees win the
series? (The series is won by the first team to win four games.)

May anyone start me off on this question? I'm feeling very dumb and do not know where to start
My apologies that I don't even have suggestions to begin with

TIA

2. Originally Posted by lindah
The Yankees are playing the Dodgers in a world series. The Yankees win each
game with probability .6. What is the probability that the Yankees win the
series? (The series is won by the first team to win four games.)

May anyone start me off on this question? I'm feeling very dumb and do not know where to start
My apologies that I don't even have suggestions to begin with

TIA
Read this: Negative binomial distribution - Wikipedia, the free encyclopedia

3. Hello, lindah!

The Yankees are playing the Dodgers in the World Series.
The Yankees win each game with probability 0.6.
What is the probability that the Yankees win the series?
(The series is won by the first team to win four games.)
Let: . $\begin{Bmatrix}W &=& \text{win} \\ L &=& \text{loss} \end{Bmatrix}$

There are 4 possible scenarios . . .

(1) They win the first 4 games: . $WWWW$
. . . $P(4W) \:=\:(0.6)^4 \:=\:0.1296$

(2) They win in the 5th game: . $LWWWW$
. . . The one Loss can occur in any of the first 4 games.
. . . $P(\text{4W, 1L}) \:=\:4(0.6)^4(0.4)^1 \:=\:0.20736$

(3) They win in the 6th game: . $LLWWWW$
. . The 2 Losses can occur in any of the first 5 games: . $_5C_2 \,=\,10$ ways..
. . . $P(4W, 2L) \:=\:10(0.6)^4(0.4)^2 \:=\:0.20736$

(4) They win in the 7th game: .LLLWWWW[/tex]
. . . The 3 Losses can occur in any of the first 6 games: . $_6C_3 \,=\,20$ ways.
. . . $P(\text{4W, 3L}) \:=\:20(0.6)^4(0.4)^3 \:=\:0.165888$

Therefore: . $P(\text{Yankees win}) \;=\;0.1296 + 0.20736 + 0.20736 + 0.165888 \;=\;\boxed{0.710208}$