The World Series in baseball is won by the first team to win 4 games (ignoring the 1903 and 1919-1921 world series, when it was a best of 9.) Thus it takes at least 4 games and no more than 7 games to establish a winner. (We are going to ignore those games in the early years that ended in a tie.) The table below gives the data on every world series from 1905-2010, with the exceptions noted above and in 1994 during the player's strike.

# of Games Frequency
4 19
5 25
6 23
7 35

a.) If X denotes the number of games that it takes to complete a World Series, identify the possible values of X, then state whether this is a discrete or a continuous random variable.

b.) Create a probability table for X.

c.) Based on past years' data, what is the probability that the 2011 series will take fewer than 6 games?

d.) Historically, what is the most likely number of games it takes to complete a series?

e.) What is the expected number of games it takes to complete a series?

f.) Why do your answers to (d) and (e) differ?