Your favorite team is in the World Series. You have assigned a probability of 64% that they will win the championship. Past records indicate that when teams win the championship, they win the first game of the series 67% of the time. When they lose the championship, they win the first game 23% of the time. The first game is over and your team has lost. What is the probability that they will win the World Series?
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the probability they win the world series and lose the first game is \[.64\times .33\] if i am not mistaken
that is the probability that they win the world series times the probability that they lose the first game given they have one the world series
that is your numerator
the denominator is the probability (percent of the times ) that they lose the first game
if the win the world series and lose the first game, that gives the same number above
if they lose the first gave and lose the world series, that is \(.36\times .23\)