12. (10 points) Timmy and his little brother set up a roadside lemonade stand. If they sell a cup of lemonade before 3:00 pm they make a profit of 80 cents. If they sell a cup between 3:00 pm and 5:00 pm they make a profit of 50 cents. After 5:00 pm they have to go home and they lose 10 cents on every cup that's not sold. Suppose they sell 70% of their lemonade before 3:00 pm and 20% between 3:00 pm and 5:00 pm. What is their expected profit per cup of lemonade?

13. (15 points) A bag contains 7 red, 5 white, and 3 blue marbles. Two marbles are drawn, one at a time, without replacement.

(a) Draw a tree diagram.

(b) Find the probability that the two marbles drawn are white and red, in that order.

(c) Find the probability that no red marbles are drawn.