# Malibu played a best-of-five series against another. The first team to win 3 times, wins the series. What is the probability that Malibu won the series if Malibu lost the 4th game of the series?

At least 4 games were played as Malibu lost game 4.

(1) If only 4 games were played then Malibu lost the series. There are 3 ways this could have happened: LLWL , LWLL, WLLL

(2) If 5 games were played then either Malibu won the series, or lost the series.

(a) There are 3 ways that Malibu could have lost the series after losing game 4: LWWLL, WLWLL, WWLLL

(b) There are 3 ways that Malibu could have won the series having lost the 4th game: WWLLW, WLWLW, LWWLW

Thus there are 9 scenarios where Malibu loses game 4. In three of those Malibu goes on to win the series.

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The probability that Malibu won the series after losing game 4 is 1/3

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