Bob and Anna are planning to meet for lunch at Sally's Restaurant, but they forgot to schedule a time. Bob and Anna are each going to randomly choose from either 1\text{ p. m.}1 p. m.1, start text, space, p, point, m, point, end text, 2\text{ p. m.}2 p. m.2, start text, space, p, point, m, point, end text, 3\text{ p. m.}3 p. m.3, start text, space, p, point, m, point, end text, or 4\text{ p. m.}4 p. m.4, start text, space, p, point, m, point, end text to show up at Sally's Restaurant. They must both choose exactly the same time in order to meet. Bob has a "buy one entree, get one entree free" coupon that he can only use if he meets up with Anna. If he successfully meets with Anna, Bob's lunch will cost him \$5$5dollar sign, 5. If they do not meet, Bob's lunch will cost him \$10$10dollar sign, 10. What is the expected cost of Bob's lunch?