Question: 1. Consider flipping a fair coin while rolling an eight-sided die. Compute the expected value of B = H +F, where H is the number of heads revealed and F = 1 when the roll is a multiple of four and F = 0 if not. Are the events H = 1 and F = 1 independent?
2. In the United States, mail is delivered six days each week. Your BFF (best friend forever) is on a trip and has sent you ten packages, all of which are scheduled to arrive this week. However, you have no idea on what day any of the packages will arrive. What is the expected number of packages that you receive on a particular weekday?