Chad and Chad2 run competing rare candy stores at Princeton. Chad has a large supply of boxes of candy, each box containing three candies and costing him \$ 3 to purchase from his supplier. He charges \$ 1.50 per candy per student. However, any rare candy in an opened box must be discarded at the end of the day at no profit. Chad knows that at each of $8$am, $10$am, noon, 2 \mathrm{pm}, 4 \mathrm{pm}, and 6 \mathrm{pm}, there will be one person who wants to buy one candy, and that they choose between Chad and Chad2 at random. (He knows that those are the only times when he might have a customer.) Chad may refuse sales to any student who asks for candy. If Chad acts optimally, his expected daily profit can be written in simplest form as \frac{m}{n}. Find m+n. (Chad’s profit is \$ 1.50 times the number of candies he sells, minus \$ 3 per box he opens.)