Human blood can be classified by the ABO blood grouping system. The four groups
ID: 3206215 • Letter: H
Question
Human blood can be classified by the ABO blood grouping system. The four groups are A, B, AB, or O, depending on whether antigens labeled A and B are present on red blood cells. Hence, the AB blood group is one where both A and B antigens are present; the O group has none of the antigens present. For three U.S. populations, the following distributions exist:
Blood Group
For simplicity, consider only the population of American blacks in the following question. The table shows that for a person selected randomly from this population, P[A] = 0.27, P[B] = 0.20, P[AB] = 0.04, and P[O] = 0.49.
(a) Calculate the probability that a person is not of blood group A.
(b) Calculate the probability that a person is either A or O. Are these mutually exclusive events?
(c) What is the probability that a person carries A antigens?
(d) What is the probability that in a marriage both husband and wife are of blood group O? What rule of probability did you use? (What assumption did you need to make?)
A B AB O Total Caucasian 0.44 0.08 0.03 0.45 1.00 American Black 0.27 0.20 0.04 0.49 1.00 Chinese 0.22 0.25 0.06 0.47 1.00Explanation / Answer
a) probability that a person is not of blood group A= 1- probability that a person is of blood group A.
= 1-0.27 =0.73
b) probability that a person is either A or O= P[A] +P[O] = 0.27, + 0.49 = 0.76
two propositions (or events) are mutually exclusive or disjoint if they cannot both be true (occur).
yes they are mutually exclusive events
c) probability that a person carries A antigens = P[A] = 0.27,
d) probability that in a marriage both husband and wife are of blood group O= P[O] * P[O] = 0.49 * 0.49 = 0.2401
Multiplication Rule
Assumption : husband and wife blood groups are independent
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