Results 1 to 3 of 3

Math Help - Bayes Probability - Yankees and World Series

  1. #1
    Junior Member
    Joined
    Nov 2009
    From
    Australia
    Posts
    56

    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
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by lindah View Post
    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
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,740
    Thanks
    645
    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}

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. (Simple) World series probability question?
    Posted in the Statistics Forum
    Replies: 4
    Last Post: March 13th 2011, 07:02 PM
  2. Probability-Bayes Theorem
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 5th 2010, 11:13 PM
  3. World series probability problem please help!
    Posted in the Statistics Forum
    Replies: 3
    Last Post: December 1st 2009, 04:24 PM
  4. Probability and Bayes' formula
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: September 28th 2008, 04:27 AM
  5. probability bayes theorem
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: April 16th 2007, 07:55 PM

Search Tags


/mathhelpforum @mathhelpforum