1. Suppose a quiz has 10 multiple choice questions. Each question has 4 answer choices. If a student takes the quiz and randomly guesses on every question.... a) Find the probability the student gets between 2 and 7, exclusive, questions correct. b) Find the probability the student gets more than 6 questions correct. 2. One state lottery has 500 prizes of $1, 75 prizes of $10, 15 prizes of $65, 5 prizes of $325, 2 prizes of $1250, and 1 prize of $2500. Assume that 21000 lottery tickets are issued and sold for $1. a) What is the lottery's expected profit per ticket? b) What is the lottery's standard deviation of profit per ticket