Exercise 1. Two dice are simultaneously rolled. For each pair of events defined below, compute if they are independent or not.

(a) A1 ={thesumis7},B1 ={thefirstdielandsa3}.

(b) A2 = {the sum is 9}, B2 = {the second die lands a 3}.

(c) A3 = {the sum is 9}, B3 = {the first die lands even}.
(d) A4 = {the sum is 9}, B4 = {the first die is less than the second}.

(e) A5 = {two dice are equal}, B5 = {the sum is 8}.
(f) A6 = {two dice are equal}, B6 = {the first die lands even}.

(g) A7 = {two dice are not equal}, B7 = {the first die is less than the second}.

Exercise 2. Are the events A1, B1 and B3 from Exercise 1 independent?

Honors Exercise. Suppose you toss a fair coin repeatedly and independently. If it comes up heads, you win a dollar, and if it comes up tails, you lose a dollar. Suppose you start with $20. What is the probability you will get to $150 before you go broke?