a) Consider that 20% of the students of a given academia engage in final presentation during the last week of semester. Moreover, assume that 40% of students are male, and 16% of all students are males who engage in final presentation during the last week of semester. i. If you choose a student at random from this academia, what is the probability that this person is a female who engage in final presentation during the last week of semester? ii. If you choose a student at random from this academia, what is the probability that this person is a male who does not engage in final presentation during the last week of semester?

b) Suppose that for a recent admissions class, a DA Degree College received 1,651 applications for early admission. Of this group, it admitted 740 students early, rejected 370 outright, and deferred 541 to the regular admission pool for further consideration. In the past, this college has admitted 28% of the deferred early admission applicants during the regular admission process. Let E, R, and D represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool. i. Use the data to estimate P(E), P(R), and P(D).ii. Are events E and D mutually exclusive? Find . iii. Suppose a student applies for early admission. What is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?