1. Two 4-sided dice are tossed and the sum of the down sides noted. A 4-sided die doesn't have an "up" face like a 6-sided die has, so the down side is used. Determine the expected value of the sum. Provide evidence of your work by typing out your full solution.

2. Two 4-sided dice are tossed 10 times and the sum of the "down" faces is noted. What is the probability that the sum of 4 occurs at most two times? Leave your answer as a percent rounded to one decimal place. Provide evidence of your work by typing out your full solution.

3. Two 4-sided dice are tossed 10 times and the sum of the "down" faces is noted. What is the expected number of times a sum of three should occur? Provide evidence of your work by typing out your full solution.

4. A drawer contains 5 pairs of green socks, 3 pairs of black socks, and 4 pairs of red socks. The 12 pairs of socks are jumbled together in one drawer, but each sock is still attached to its mate. You reach into the drawer and pull out 3 pairs of socks, one at a time, without putting any back. What is the probability that you get 2 pairs of green socks? Leave your answer as a fraction in lowest terms. Provide evidence of your work by typing out your full solution.

5. A drawer contains 5 pairs of green socks, 3 pairs of black socks, and 4 pairs of red socks. The 12 pairs of socks are jumbled together in one drawer, but each sock is still attached to its mate. You reach into the drawer and pull out 3 pairs of socks, one at a time, without putting any back. What is the expected number of pairs of green socks? Provide evidence of your work by typing out your full solution.

6. In Chelmsford County Hospital, the probability that a randomly chosen birth results in a boy is 45%. Over the course of a month, there are 20 births at the hospital.Is a normal approximation to the binomial distribution appropriate here? Show your calculations and explain your choice.

7. In Chelmsford County Hospital, the probability that a randomly chosen birth results in a boy is 45%. Over the course of a month, there are 20 births at the hospital. What is the chance that more than 14 of the births are boys? Use the method of the normal approximation to the binomial distribution. Provide evidence of your work by typing out your full solution.

8. In Chelmsford County Hospital, the probability that a randomly chosen birth results in a boy is 45%. Over the course of a month, there are 20 births at the hospital. What is the chance that more than 14 of the births are boys? Use the binomial distribution formula. Provide evidence of your work by typing out your full solution.