Professor Weiss has 40 students, 17 of whom are male. He selects 2 students. What's the probability that the first student selected is male and the second is female? Assume that a student who has been selected cannot be selected again. (This is called sampling without replacement.) 17/40 x 22/39 O 23/40 x 17/39 O 17/40 x 23/40 O 17/40 x 23/39 Question 2 1 pts Suppose 45% in a certain group of COVID-19 patients is female. In this same group, the prevalence of diabetes among the females is 25%. To find the probability that a randomly selected individual in this group is a diabetic female, which expression is useful? In the choices below, let A be the event that a COVID-19 patient is female and B be the event that a COVID-19 patient is diabetic. O P(A) P(BIA) O P(A) + P(B) O P(A) P(B) O P(A) + P(B) - P(A & B) Question 3 1 pts Given: A and B are not null events. Which events are mutually exclusive? O Event 1: A, Event 2: A & B O Event 1: A\\B, Event 2: B\\A O Event 1: A & B, Event 2: A O Event 1: A & B, Event 2: A or BQuestion 4 1 pts If A and B are mutually exclusive, which of the following statements is necessarily true? I. A U B must be the impossible event (i.e., empty). Il. An B must be the impossible event (i.e., empty). III. P(A U B) must be 0. IV. P(An B) must be O. V. P(A | B) must be O. O I, II and Ill only O II, IV and V only O II and IV only O I and Ill only Question 5 1 pts Consider two events A and B, neither of which is the null event. If events A and B are independent, P(A|B) = P(A). Alternatively, P(BIA) = P(B). If A and B are mutually exclusive, what is P(A|B)? O P(A) P(B) O 1 O P(A) + P(B) OOQuestion 6 1 pts Consider the population of all patients who underwent aortic valve replacement. Select a patient randomly from this population. Let A be the event that the patient had a post-operative heart attack. Let B be the event that the patient is female. What is the complement of P(A | B)? O P(A | not B) O P(not A) O P(not A | not B) O P(not A | B)Question 7 1 pts Myocardial Infarction (MI) Treatment Yes No Total Aspirin 104 10933 11037 Placebo 189 10845 11034 Total 293 21778 22071 These are the results from a clinical trial that investigated whether taking aspirin (Asp vs Pla) reduces the risk of a heart attack (MI vs NoMI). To address this question, which conditional probabilities should be compared? O P(MI | Asp) and P(NoMI | Asp) O P(Asp | MI) and P(Pla | MI) O P(MI | Asp) and P(MI | Pla) O P(MI | Pla) and P(NoMI | Pla)Question 8 1 pts Aspirin Total a+ la+b+c+d I I r The 2 x 2 table above can help us evaluate the association between taking aspirin and the occurrence of a heart attack (MI). Assume that the table above represents the entire population. Note that the risk of having an MI in the population is (a+c)f(a+b+c+d). If taking aspirin is independent of having an MI, which statement is correct? I. the risk of having an MI in the aspirin group is afiai-b], which should be very different from (a+c]/(a+b+c+d] II. the risk of having an MI in the aspirin group is a/[a+b), which should be equal to (a+c]/{a+b+c+dl Oll O l