Exercise 3. [25 points] Sample Space and Independence A graduating engineer has signed up for three job interviews, She intends to categorize each one as being either a "success" or a "failure" depending on whether it leads to a plant trip. a) Write out the appropriate sample space for the three job interviews "random experiment." (5 points]b) How many numbers do you need to know to completely specify this probability distribution? Remem ber, it is enough to specify what is the probability of each point in the sample space, [5 points) c) How does your answer to part b) change if you learn that each internship outcome is independent of all others? (5 points] d) How does your answer to part b) change if you learn that each internship outcome is independent of all others and that the three internship outcomes follow the same distribution? (5 points]b) How many numbers do you need to know to completely specify this probability distribution? Remem ber, it is enough to specify what is the probability of each point in the sample space, [5 points) c) How does your answer to part b) change if you learn that each internship outcome is independent of all others? (5 points] d) How does your answer to part b) change if you learn that each internship outcome is independent of all others and that the three internship outcomes follow the same distribution? (5 points]e) Give your reasoning on why you believe it is unrealistic to assume that the interview outcomes are independent. [5 points]