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4. Suppose an experiment consists of picking a student from the set of all students registered on the UCSD campus this quarter. It is not necessary to assume that all students are equally likely to be picked, but you may make this assumption if it makes you feel happier and more confident. (a) Consider the two events: Athe student has had four years of high school science (FYS), Bthe student has had calculus in high school. If the probability that he/she has had at least one of FYS and calculus is 0.7, and the bility that he/she has missed at least one of the two is 0.8, what is the probability that he/she has had exactly one of the two? (b) Let C denote the event that the student is registered in ECE109 this quarter, and let events A and B and their probabilities be as in part (a). If students who had had at most one of FYS and calculus did not register in ECE109 this quarter, i. What is P(A n BEnc)? ii. What is the probability that the student picked is not registered in ECE109 and has had exactly one of FYS or calculus in high school? (c) Using the data given in parts (a) and (b), which of the following probabilities: P(ABC), PC), P(A BC), P(A), P(A BC), P(AUBUCe) can you compute? It is not necessary to actually compute each probability.

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