Concept explainers
Blood Types and Rh Factors In addition to being grouped into four types, human blood is grouped by its Rhesus (Rh) factor. Consider the figures below which show the distributions of these groups for Americans.
Choose one American at random. Find the probability that the person
a. Is a universal donor, i.e., has O-negative blood
b. Has type O blood given that the person is Rh+
c. Has A+ or AB− blood
d. Has Rh− given that the person has type B
a.
To obtain: The probability that the person has O– blood group.
Answer to Problem 31E
The probability that the person has O– blood group is 0.06.
Explanation of Solution
Given info:
The data shows that the distributions of types of blood groupsand Rh factors for Americans.
Calculation:
The total number of Rh factors is shown in the Table (1).
O | A | B | AB | Total | |
Rh+ | 37 | 34 | 10 | 4 | 85 |
Rh– | 6 | 6 | 2 | 1 | 15 |
Total | 43 | 40 | 12 | 5 | 100 |
Table (1)
Let event A denote that the person has O– blood group.
The formula for probability of event A is,
Substitute 6 for ‘Number of outcomes in A’ and 100 for ‘Total number of outcomes in the sample space’,
Thus, the probability that the person has O– blood group is 0.06.
b.
To obtain: The probability that person has type O blood given that the person has Rh+ factor.
Answer to Problem 31E
The probability that the person has type O blood given that the person has Rh+ factoris 0.435.
Explanation of Solution
Calculation:
Let event B denote that thethe person has Rh+ factorand event C denote that the person has type O blood.
The probability of event B is,
Substitute 85 for ‘Number of outcomes in B’ and 100 for ‘Total number of outcomes in the sample space’,
The formula for probability of event B and C is,
Substitute 37 for ‘Number of outcomes in B and C’ and 100 for ‘Total number of outcomes in the sample space’,
Conditional rule:
The formula for probability of C given B is,
Substitute 0.82 for
Thus, the probability that the person has type O blood given that the person has Rh+ factor is 0.435.
c.
To obtain: The probability that person has type A+ blood or the person hasAB–.
Answer to Problem 31E
The probability that person has type A+ blood or the person hasAB– is 0.35.
Explanation of Solution
Calculation:
Let event D denote that the the person hasA+ blood and event E denote that the person has type AB–blood. Also, the event E does not affected by the event D.
The probability of event D is,
Substitute 34 for ‘Number of outcomes in D’ and100 for ‘Total number of outcomes in the sample space’,
The probability of event E is,
Substitute 1 for ‘Number of outcomes in C’ and 100 for ‘Total number of outcomes in the sample space’,
Addition Rule:
The formula for probability of getting event A or event B is,
Substitute 0.34 for
Thus, theprobability that person has type A+ blood or the person hasAB– is 0.35.
d.
To obtain: The probability that person has type Rh– factor given that the person hasB blood.
Answer to Problem 31E
The probability that person has type Rh– factor given that the person hasB blood is 0.167.
Explanation of Solution
Calculation:
Let event F denote that the the person hasB bloodand event G denote that the person hasRh– factor.
The probability of event F is,
Substitute 12 for ‘Number of outcomes in F’ and 100 for ‘Total number of outcomes in the sample space’,
The formula for probability of event F and G is,
Substitute 2 for ‘Number of outcomes in F and G’ and 100 for ‘Total number of outcomes in the sample space’,
Conditional rule:
The formula for probability of G given F is,
Substitute 0.12 for
Thus, the probability that the person has type Rh– factor given that the person hasB blood is 0.167.
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