Problem 1. Danny has two fair dice; one is eight-sided, and the other is ten-sided. He tosses them at the same time. (a) What is the probability of obtaining a one and a three (which die gave which number is irrelevant)? (b) What is the probability that the sum of the numbers he gets is even? (c) What is the probability that the sum of the numbers he gets is a multiple of 3?

Problem 2. Consider the numbers from one up to one trillion (1, 000, 000, 000, 000). (a) How many of these numbers do not have 9 as a digit? (b) We choose a number from the list at random. What is the probability of my number being even? (c) We choose two distinct numbers from the list at random. What is the probability of one of them being even?

Problem 3. Suppose that the grades of the 131 students in Math in Action are assigned at random (between A,B,C,D,E, and F). (a) What is the probability of everyone getting an A? (b) What is the probability of exactly 120 students passing the class (passing grade is E or higher)? (c) What is the probability of 100 students getting As, 20 Bs, and 11 Cs?

Problem 4. The Consulate of Mexico is on the corner of Park Ave and E 39th St, and The Empire State Building is at the intersection of 5th Av with E 34th St (see map below). Jose is only walking from the Consulate to the Empire State. He does not want to repeat streets and only wants to walk seven blocks. How many possible routes can Jose take?