1. From Anderson et a14.27 (pg 191): The Atlantic Coast Conference (ACC) had 10 teams in the NCAA basketball championship game in the last 20 years. The Southeastern Conference (SEC) had 8 teams in the championship in the last 20 years. In 1 year, both the ACC and SEC had teams in the championship game. Using this data, calculate the following
a. The probability the ACC will have a team in the championship game.
b. The probability the SEC will have a team in the championship game.
c. The probability they will both have a team in the championship game.
d. The probability that at least one team from either conference will be in the championship game
e. The probability that neither conference will have a team in the championship game.
2. Mega Millions is a Massachusetts state lottery game where there are two drawings. In the first drawing, five numbers are chosen from {1,2,...,56} (assume that if a number is chosen, it cannot be chosen again). In the second drawing, one number, called the "Megaball", is chosen from {1,2,...,46). Assume that Mega Millions and Megaball are statistically independent from each other. Also, assume that order does not matter; just what is selected matters.
a. Including both drawings, how many different basic outcomes are in the sample space?
b. If you buy one ticket, what is the probability of matching all five numbers in the first drawing and not matching the Megaball?
c. Suppose the first three numbers of the first drawing are called and your ticket matches all three. What is the probability your ticket will match the rest of the numbers (including the Megaball)?