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Math

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In a World Series, two teams play each other in at least four and at most seven games. The first team to win four games is the winner of the World Series. Assuming that both teams are equally matched, what is the probability that a World Series will be one (a) in four games? (b) in five games? (c) in six games? (d) in seven games? Explain.

  • Math -

    Be "equally matched" I will assume
    P(win) = 1/2 = prob(loss)

    winning in 4 games = (1/2)^4 = 1/16

    in 5 games, has to lose once)
    LWWWW
    WLWWW
    WWLWW
    WWWLW ----- each of these has a prob of (1/2)^5
    but there are 4 cases,
    so prob(5games) = 4/32 = 1/8

    6 games , 2 losses, 4 wins
    number of ways = 6!/(2!4!) = 15 , but that includes the case of ending with a loss, which can't happen
    so number of 6 games is 14
    prob(6games) = 14/(1/2)^6 = 14/64 = 7/32

    7 games, 4 wins, 3 losses
    number of cases = 7!/(3!4!) = 35 , less the case of ending in L
    we have 34 such cases
    prob(7 games) = 34/(1/2)^7 = 34/128 = 17/64

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