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example test

# example test - Midterm Exam Wednesday Oct 14 2009 1 A...

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Midterm Exam Wednesday, Oct. 14, 2009 1. A simplified model of the human blood-type system has four blood types: A, B, AB, and O. There are two antigens, anti-A and anti-B, that react with a person’s blood in different ways depending on the blood type. Anti-A reacts with blood types A and AB, but not with B and O. Anti-B reacts with blood types B and AB, but not with A and O. Suppose that a person’s blood is sampled and tested with the two antigens. Let A be the event that the blood reacts with anti-A, and let B be the event that it reacts with anti-B. Classify the person’s blood type using the events A, B, and their complements. Solution: Blood type A reacts only with anti-A, so type A blood corre- sponds to AB c . Type B blood reacts only with anti-B, so type B blood corresponds to A c B . Type AB blood reacts with both, so AB character- izes type AB blood. Finally, type O reacts with neither antigen, so type O blood corresponds to the event A c B c . 2. Consider, once again, problem 1. Suppose that, for a given person, the probability of type O blood is 0.5, the probability of type A blood is 0.34, and the probability of type B blood is 0.12. (a) Find the probability that each of the antigens will react with this person’s blood. (b) Find the probability that both antigens will react with this person’s blood. Solution: First note that the probability of type AB blood is 1 - (0 . 5 + 0 . 34 + 0 . 12) = 0 . 04.

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example test - Midterm Exam Wednesday Oct 14 2009 1 A...

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