You are participating in the candidate weekend on campus and a prospect student approaches you. She tells you that she is interested in Political Science and she would like to know more about the career prospects, but that she hasn't met anyone who graduated with a Political Science major yet. The three NYUAD Social Science graduates that she met before all graduated with an Economics major. You wonder what the chances are. To answer her questions, you look at results from a survey conducted by the university about social science majors and their career prospects. Assume that all NYUAD graduates either go to grad school or to the private sector. Major Share of graduates in the Social Sciences in 2016 0.4 Share that went to Grad School afterwards (2016/2017) Average Income in USD of students who went to the private sector afterwards (2016/2017) 70,000 60,000 Economics 0.8 Political Science 0.3 0.6 SRPP 0.3 0.7 150,000 a) What are the possible events if you randomly choose a recent Social Science graduate? Define the probabilities that a randomly chosen graduate studied Economics (A), Political Science (B) or SRPP (C). What is the probability that a graduate studied either SRPP or Economics? What is the probability that a student did not study Economics? (4 points) b) You wonder how likely it is that the candidate met three Econ graduates. Calculate the probability of meeting three Econ graduates if you only meet three graduates. On campus everyone seems to study SRPP: What are the chances of not meeting any SRPP graduate if you meet three recent graduates? (5 points) c) What is the conditional probability that an Econ graduate went to grad school in 2016/2017 (define going to Grad School as event G)? What is the conditional probability that an SRPP graduate went to grad school? What is the conditional probability that a Political Science graduate went to grad school? (4 points) d) Imagine you meet a Social Science PhD student in Grad School who went to NYUAD. What is the probability that this student studied Political Science? (5 points) e) Suppose those who did go to grad school have an income of 0 USD (because they all receive stipends). What is the expected average income for an Economics graduate? (5 points)