Midterm Exam
Wednesday, Oct. 14, 2009
1. A simplified model of the human bloodtype system has four blood types:
A, B, AB, and O. There are two antigens, antiA and antiB, that react
with a person’s blood in different ways depending on the blood type.
AntiA reacts with blood types A and AB, but not with B and O. AntiB
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 antiA, and let B be the event that
it reacts with antiB. Classify the person’s blood type using the events A,
B, and their complements.
Solution:
Blood type A reacts only with antiA, so type A blood corre
sponds to
AB
c
. Type B blood reacts only with antiB, 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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 Spring '08
 Staff
 Normal Distribution, Probability, Probability theory, ABO blood group system

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