Concept explainers
(a)
To find the probability that the specimen contains type O blood or comes from the Hawaiian-Chinese ethnic group.
(a)
Answer to Problem 23PT2
Explanation of Solution
In the question it is given there are four major types in humans: O, A, B and AB. In a study conducted using blood specimens for the blood bank of Hawaii are classified according to blood type and ethnic groups such as Hawaiian (H), Hawaiian-White (HW), Hawaiian-Chinese (HC) and white (W). Thus, we have to find the probability that the specimen contains type O blood or comes from the Hawaiian-Chinese ethnic group, that is,
Thus, from the table we have that,
Ethnic group | |||||
Blood Type | H | HW | HC | W | Total |
O | 1903 | 4469 | 2206 | 53759 | 62337 |
A | 2490 | 4671 | 2368 | 50008 | 59537 |
B | 178 | 606 | 568 | 16252 | 17604 |
AB | 99 | 236 | 243 | 5001 | 5579 |
Total | 4670 | 9982 | 5385 | 125020 | 145057 |
Thus, we have,
(b)
To find out what is the probability that the specimen contains type AB blood, given that it comes from the Hawaiian ethic group.
(b)
Answer to Problem 23PT2
Explanation of Solution
In the question it is given there are four major types in humans: O, A, B and AB. In a study conducted using blood specimens for the blood bank of Hawaii are classified according to blood type and ethnic groups such as Hawaiian (H), Hawaiian-White (HW), Hawaiian-Chinese (HC) and white (W). Thus, we have to find the probability that the specimen contains type AB blood, given that it comes from the Hawaiian ethic group, that is,
Thus, from the table we have that,
Ethnic group | |||||
Blood Type | H | HW | HC | W | Total |
O | 1903 | 4469 | 2206 | 53759 | 62337 |
A | 2490 | 4671 | 2368 | 50008 | 59537 |
B | 178 | 606 | 568 | 16252 | 17604 |
AB | 99 | 236 | 243 | 5001 | 5579 |
Total | 4670 | 9982 | 5385 | 125020 | 145057 |
Thus, we have,
(c)
To find out are the
(c)
Answer to Problem 23PT2
They are not independent.
Explanation of Solution
In the question it is given there are four major types in humans: O, A, B and AB. In a study conducted using blood specimens for the blood bank of Hawaii are classified according to blood type and ethnic groups such as Hawaiian (H), Hawaiian-White (HW), Hawaiian-Chinese (HC) and white (W).
Thus, from the table we have that,
Ethnic group | |||||
Blood Type | H | HW | HC | W | Total |
O | 1903 | 4469 | 2206 | 53759 | 62337 |
A | 2490 | 4671 | 2368 | 50008 | 59537 |
B | 178 | 606 | 568 | 16252 | 17604 |
AB | 99 | 236 | 243 | 5001 | 5579 |
Total | 4670 | 9982 | 5385 | 125020 | 145057 |
Thus, we have,
The probability of having a blood group type B is then,
And the probability of Hawaiians having blood group B is as:
Thus, the probabilities of both the above two should be identical if the two events are independent. Since the two probabilities are not identical, this then implies that the events “having blood type B” and “Hawaiian ethnic group” are not independent.
(d)
To find the probability that at least one of the specimens contains type A blood from the White ethnic group.
(d)
Answer to Problem 23PT2
Explanation of Solution
In the question it is given there are four major types in humans: O, A, B and AB. In a study conducted using blood specimens for the blood bank of Hawaii are classified according to blood type and ethnic groups such as Hawaiian (H), Hawaiian-White (HW), Hawaiian-Chinese (HC) and white (W).
Thus, from the table we have that,
Ethnic group | |||||
Blood Type | H | HW | HC | W | Total |
O | 1903 | 4469 | 2206 | 53759 | 62337 |
A | 2490 | 4671 | 2368 | 50008 | 59537 |
B | 178 | 606 | 568 | 16252 | 17604 |
AB | 99 | 236 | 243 | 5001 | 5579 |
Total | 4670 | 9982 | 5385 | 125020 | 145057 |
Thus, when two specimens are drawn at random, one of 4 things can happen, that is, both are A and W; the first is from A and W, the second is not; The first is not A and W, the second is; Neither are from A and W. These are the only four cases which means their probabilities add up to one. Notice that if we wanted to calculate the probability, case
And given that the first draw did not get A from W, there are
Since we want the probability that both events happen, use the multiplication rule, as follows,
And thus we have,
Chapter 7 Solutions
The Practice of Statistics for AP - 4th Edition
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Statistics: The Art and Science of Learning from Data (4th Edition)
Intro Stats
Elementary Statistics Using Excel (6th Edition)
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