Question 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(B|A) = 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)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 9 1 pts Study the SAS code below. The data set comes from male subjects in their 205 and contains information about their heights in inches and also their heights converted to centimeters. Describe what you expect to see in the output without running 5A5. proc means data=s.heights n mean std cv: var height_in height_cm; run: 0 The mean, standard deviation and coefcient of variation of height measured in inches are equal. respectively. in value to the mean, standard deviation and coefcient of variation of height measured in centimeters. O The coefcient of variation of height measured in inches is equal in value to the coefcient of variation of height measured in centimeters. However, the means and standard deviations have different values. 0 The standard deviation and coefcient of variation of height measured in inches are equal, respectively, in value to the standard deviation and coefcient of variation of height measured in centimeters. However, the means have different values. O The mean, standard deviation and coefcient of variation of height measured in inches are not equal in value, respectively, to the mean, standard deviation and coefcient of variation of height measured in centimeters. Question 10 1 pts John Hinckley attempted to assassinate President Reagan in 1931. At the trialr the defense described that Hinckley's brain scan showed brain atrophyr which could be evidence of schizophrenia. About 1.5% of Americans suffer from schizophrenia. Brain atrophy is observed in 30% of schizophrenics. but only in 2% of normal individuals. How convincing is this argument? The answer lies in the probability that Hinckley had schizophrenia, given the evidence of brain atrophy. Find this probability. 0 0.136 O 0.424 o 0.016 0 0.234 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)/(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 a/(a+b], which should be very different from (a+c]I(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 OII O l