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Question: human blood can be classified into the four blood types...

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Human blood can be classified into the four blood types A, B, AB, and O, where: A indicates that only the A antigen is present. B indicates that only the B antigen is present . AB indicates both the A and B antigens are present O indicates neither antigen is present Suppose that for a population in the US, the probability of having the blood types A, B, and O is estimated to be: Pr(A) 0.44, Pr(B)-0.08, and Pr(O)0.45, respectively (a) Calculate the probability that a person has both A and B antigens (i.e., blood type AB). Are the blood types, A, B, AB, and O mutually exclusive? (b) Calculate the probability that a person does not have the A antigen (c) Calculate the probability that a person is either blood type A or blood type O. (d) What is the probability that you and a classmate are both blood type O? (e) You are told a patient has at least the A antigen. What is the probability that the patient also has the B antigen? (Hint: the information that the patient has the A antigen has reduced the sample space.)

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