On graduating you have found a position as a junior lecturer in industrial engineering at a local university. You are lecturing the subject Operational Research to two under graduate classes. The course OTE201S consists of 7 senior students and 3 first year students. The more advanced course OTE301S has 2 senior students and 8 first year students. You have prepared index cards for all the students that you are lecturing. From the index cards for OTE201S you have selected randomly one card and then return it to the stack. If the card selected represented a senior student, you draw another card from the same stack. If the card selected represented a junior student you would select a card from the OTE201S stack of cards. You are required to: a. Are these two events independent? Justify your answer. No marks will be awarded for a yes or no answer only. (7) b. Formulate an equation and compute the probability that a junior’s name would be selected first. (3) c. Formulate an equation and compute the probability that a junior’s name would be selected on the second draw, given that a senior’s name was selected on the first draw. (2) d. Formulate an equation and compute the probability that a junior’s name would be selected on the second draw, given that a junior’s name was selected on the first draw. (2) e. Formulate an equation and compute the probability that a senior’s name would be selected during both draws. (4)