4 Room 1 contains 5 undergraduate students and 5 graduate students, all from JHU, Room 2 contains 16 undergraduate students and 4 graduate students, all from University of Maryland. One random person is selected (independently) from each room and then both people are brought to the (previously empty) Room 3. So, Room 3 will eventually contain 2 people. Once the 2 people are in Room 3 they compete in a series of challenges in which the winner receives a prize. Assume that the JHU contestant always has a 70% chance of winning the prize over the Maryland contestant (regardless of whether the contestants are undergraduates or graduates). a.) Suppose the 2 students who compete for the prize are one undergraduate student and one graduate student. Determine the probability that the undergraduate student is from JHU. b.) Determine the probability that a graduate student wins the prize. c.) Determine the probability that a JHU student wins the prize given that a graduate student wins the prize