Math 370X - Quiz 2Saumil PadhyaSeptember 12, 2016Name Net ID1.Let A, B, C and D ve events such that B = Ac, C∩D =∅, and P(A) =14, P(B) =34, P(C|A)=12, P(C|B) =34, P(D|A) =14, P(D|B) =18. Calculate P(C ∪ D).(A)532(B)14(C)2732(D)34(E) 12.Upon arrival at a hospital’s emergency room, patients are categorized according to theircondition as critical, serious, or stable. In the past year:(i) 10% of the emergency room patients were critical(ii) 30% of the emergency room patients were serious(iii) the rest of the emergency room patients were stable(iv) 40% of the critical patients died(v) 10% of the serious patients died(vi) 1% of the stable patients diedGiven that a patient survived, what is the probability that the patient was categorized as seriousupon arrival?(A) 0.06(B) 0.29(C) 0.30(D) 0.39(E) 0.6413.An actuary is studying the prevalence of three health risk factors, denoted by A, B, and C,within a population of women. For each of the three factors, the probability is 0.1 that awoman in the population has only this risk factor (and no others). For any two of the threefactors, the probability is 0.12 that she has exactly these two risk factors (but not the other).The probability that a woman has all three risk factors, given that she has A and B, is13.What is the probability that a woman has none of the three risk factors, given that she doesnot have risk factor A?(A) 0.280(B) 0.311(C) 0.467(D) 0.484(E) 0.7004.An insurance company determines that N the number of claims received in a week, is arandom variable with P(N = n) =12n+1, where n≥0. The company also determines that thenumber of claims received in a given week is independent of the number of claims received inany other week. Determine the probability that exactly seven claims will be received duringa given two-week
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