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MATH 1107 Elementary Statistics Lecture 5 Addition Rules in Probability Addition Rules in Probability Lets say that in order to maintain your HOPE scholarship, you must obtain either an A or a B in this class. Putting aside study time and unforeseen events, what is the probability of this occurring? Addition Rules in Probability Since you cannot obtain both an A and a B, these are mutually exclusive events…or disjointed events So, the Prob (A or B) = P(A)+P(B) If your grade is random, then the answer is: Prob (A or B) = 1/5 + 1/5 = 2/5 or 40% Addition Rules in Probability Now lets say that in order to retain your scholarship, you must pass either Statistics or English. What is the probability of this? Addition Rules in Probability Since you can obtain passing grades in both, this is not considered a disjointed event. The probability for this outcome is: P(A or B) = P(A) + P(B) – P(A and B), where P(A and B) is the probability of passing both courses. This probability must be deleted to prevent double counting. Addition Rules in Probability P(A) P(A and B) P(B) Addition Rules in Probability Passengers on the Titanic Men Women Boys Girls Total Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 56 2223 What is the probability of selecting a man or a boy from the passenger list at random (regardless of their eventual fate)? Addition Rules in Probability Passengers on the Titanic Men Women Boys Girls Total Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 56 2223 P(man or boy) = 1692 + 64 = 1756 or 79% 2223 2223 2223 This is an example of a disjointed events. Addition Rules in Probability Passengers on the Titanic Men Women Boys Girls Total Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 56 2223 What is the probability of selecting a man or a survivor from the passenger list at random? Addition Rules in Probability Passengers on the Titanic Men Women Boys Girls Total Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 56 2223 P(man or survivor) = 1692 + 706 - 332 = 2066 or 93% 2223 2223 2223 2223 This is an example of events that are not disjointed. Addition Rules in Probability What is the probability of selecting a subject who is pregnant or tested positive? Positive Test Negative Test Pregnant 80 5 Not Pregnant 3 11 P(Preg or + Test) = 80 + 5 + 3 = 88 or 89% 99 99 99 99 P(Preg or + Test) = 83 + 85 - 80 = 88 or 89% 99 99 99 99 Addition Rules in Probability Positive Test Negative Test Pregnant 80 5 Not Pregnant 3 11 False Positive False Negative
