A fantasy sports league is making up their season schedule. The league has 12 teams, with eight teams from Purdue, and the rest from IU. If we assume each team's opponents are randomly assigned but they cannot play with the any of the other teams more than once. Each team has 6 games in a season. Pete is in this league and he is from Purdue. Pete is trying to figure out some probabilities related to the season schedule for his team. (Note: even though there are 12 teams, Pete's team cannot play itself.)
a) Let X be the number of teams from IU on Pete's season schedule. What's the probability that none of the Pete's opponents are from IU? What distribution and parameter(s) are you using?
b) What's the probability that 2 or 3 of the Pete's opponents are from IU?
c) How many of Pete's opponents does he expect to be from Purdue?
d) Knowing that at least 2 of Pete's opponent are from the Purdue, what is the probability that between 3 and 5 (inclusive) are from Purdue?