Two students decide to make bets about their plans for lunch during the next work week (Monday through Friday). They roll a six-sided die five times (once for each day). The agreement is that, for each day, when a 6 shows up, the first student has to pay for both lunches, and if a 1 shows up, the second student has to pay for both lunches. If neither of these events occurs, they will bring their lunch from home on that day.
a. How many days does the first student expect to buy lunch for the second student?
b. How many days do they expect to bring their lunches?
c. What is the mass of the number of days on which the first student buys lunch for the second student?