The World Series is a postseason play-off series between the two respective champions of the two major professional base

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The World Series is a postseason play-off series between the tworespective champions of the two major professional baseball leaguesin North America: the American League (AL) and the National League(NL), which together constitute Major League Baseball. The WorldSeries is a best-of-seven playoff; i.e., it consists of at most 7games and the first team to win 4 games wins the championship. Itis not necessary for the games to be won consecutively and drawsare not permitted. Once a winner is decided, the Seriesends. Suppose the two teams in the World Series have an equalprobability of winning each of the 7 games and that the games areindependent.
Calculate the probability that the World Series ends in 4 games,5 games, 6 games, and 7 games. Let X represent the number of gamesthat the World Series will consist of this year. Compute the meanand variance of X.