Part I: Probability For each of the following problems, you should write your answer as an expression. Do not give the final numeric value. For example, you should write C(4,2)/24 instead of 0.375. 2. The Powerball lottery is based on a random drawing of six balls from two machines. One machine contains 69 white balls (labeled 1 through 69) and the other machine contains 26 red balls (labeled 1 through 26). To determine the winning numbers, the gamemaster draws five white balls from the first machine and one red ball (the "Powerball") from the second machine (assume all outcomes are equally likely). A player in the Powerball lottery picks five different numbers between 1 and 69 (inclusive) and a sixth number between 1 and 26 (inclusive), which may duplicate one of the first five numbers. 2.1 A player wins the jackpot ($98 million) if the first five numbers picked match the numbers on the five white balls (in any order) and the sixth number picked matches the number on the red ball. What is the probability that a player wins the jackpot? 2.2 What is the probability that a player wins $100 by matching exactly four of the first five numbers (in any order), but not the sixth number? 2.3 What is the probability that a player wins $4 by matching the sixth number and at most one of the first five numbers?