The World Series in baseball is won by the first team to win four games (ignoring the 1903 and 1919-1921 World Series, when it was a best of nine). Thus it takes at least four games and no more than seven games to establish a winner. From the document World Series History on the Baseball Almanac website, as of November 2013, the lengths of the World Series are as given in the following table.

a. If X denotes the number of games that it takes to complete a World Series, identify the possible values of the random variable X.
b. Do the first and third columns of the table provide a probability distribution for X? Explain your answer.
c. Historically, what is the most likely number of games it takes to complete a series?
d. Historically, for a randomly chosen series, what is the probability that it ends in five games?
e. Historically, for a randomly chosen series, what is the probability that it ends in five or more games?
f. The data in the table exhibit a statistical oddity. If the two teams in a series are evenly matched and one team is ahead three games to two, either team has the same chance of winning game number six. Thus there should be about an equal number of six- and seven-game series. If the teams are not evenly matched, the series should tend to be shorter, ending in six or fewer games, not seven games. Can you explain why the series tend to last longer than expected?

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Number (ที่โ Relative of games Frequency frequency 21 24 24 36 0.200 0.229 าว 4 6 0.229 0.343