HW 5B - HW 5E Solutions (1)
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University at Buffalo *
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119
Subject
Mathematics
Date
Apr 3, 2024
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docx
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6
Uploaded by EarlPorcupineMaster1036
HW5B (1): Name ______________________________ Class Number _________________ As in the class notes, a survey is conducted and tabulated below.
Blood
Typ
e
Total
Ethnic
Group
O
A
B
AB
G1
225
250
200
50
725
G2
800
75
100
25
1000
G3
150
350
125
60
685
Total
1175
675
425
135
2410
A person from this survey is chosen at random. Answer the questions below. Do not reduce the fractions!!
1. P(G1) 2. P(Type A Blood)
3. P(Type B Blood G3)
4. P(G1 Type AB Blood)
5. P(Type A or Type O Blood) 6. P(The person is from group G2 and has Type AB Blood)
7. P(The person is not from group G2)
8. P(G1 G2)
HW5C (1): Name ______________________________ Class Number _________________ As in the class notes, a survey is conducted and tabulated below.
Blood
Typ
e
Total
Ethnic
Group
O
A
B
AB
G1
225
250
200
50
725
G2
800
75
100
25
1000
G3
150
350
125
60
685
Total
1175
675
425
135
2410
A person from this survey is chosen at random. Answer the questions below. Do not reduce the fractions!!
Since these are conditional probabilities, the denominators will not be 2410. Recall that when
answering conditional probability questions we have 1. P(G1 | Type O Blood)
2. P(Type O Blood | G1)
3. P(Not Type AB Blood | G3)
4. P[(G1
G3) | Type B Blood]
5. P(G2 | Type A Blood)
6. P(Type A Blood | Type B Blood)
HW5C (2): Name ______________________________ Class Number _________________ Data is collected on 1277 individuals from a large university that attended a clinic. Their person type and injury
type are noted and tabulated below. (Same as HW3B)
Injury
Type
Total
Person
Type
Minor Fracture
Severe
Fractur
e
Minor Joint
Severe
Joint
Male Athlete
123
29
225
46
423
Male Non-Athlete
131
16
238
18
403
Female Athlete
98
13
67
19
197
Female Non-Athlete
86
8
138
22
254
Total
438
66
668
105
1277
A person from this survey is chosen at random. Answer the questions below. Do not reduce the fractions!!
a) P(Minor Fracture | Female Athlete)
b) P(Female Athlete | Minor Fracture)
c) P(Severe Joint | Male Non-Athlete)
d) P(Male Athlete | Severe Fracture)
e) P(Male | Minor Joint)
f) P(Severe Joint | Female)
g) P(Female | Severe Injury)
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h) P(Fracture | Male)
The answers are left like this for instructional purposes. Be sure to actually add them for credit on a quiz or exam!!
i) One of the male patients is awaiting a checkup. What is the probability that this patient has a fracture? Same as h.
HW5C (3): Name ______________________________ Class Number _________________ 1. Data is gathered from a university graduate program. Data is collected from each person applying to the program. Of the 400 male applicants, 100 were accepted. Of the 400 female applicants 60 were accepted.
Not accepted
Accepted
Total
Male
300
100
400
Female
340
60
400
Total
a)
Determine P(Accepted | Male) b)
Determine P(Accepted | Female)
c) Comparing the answers in part a and b, do things seem a bit unfair at the university?
YES
2. Data is gathered from a university graduate program in the School of Science. Of the 300 male applicants, 92 were accepted. Of the 100 female applicants 35 were accepted.
Not accepted
Accepted
Total
Male
208
92
300
Female
65
35
100
Total
a)
Determine P(Accepted | Male) b)
Determine P(Accepted | Female)
I am putting in decimal form for easy comparison.
c) Comparing the answers in parts a and b, do things seem a bit unfair in the School of Science? NO
3. Data is gathered from a university graduate program in the School of Liberal Arts. Of the 100 male applicants, 8 were accepted. Of the 300 female applicants 25 were accepted.
Not accepted
Accepted
Total
Male
92
8
100
Female
275
25
300
Total
a)
Determine P(Accepted | Male) b)
Determine P(Accepted | Female)
c) Comparing the answers in part a and b, do things seem a bit unfair in the Liberal Arts School? NO
Note that if you “add” Table 2 and Table 3 together you get Table 1. It is interesting that the female probability is higher in each of the schools, but lower in the university as a whole. Simpson’s Paradox!
HW5D (1): Name ______________________________ Class Number _________________ 1. Suppose that it is known that a certain disease occurs in 1% of the population. Suppose also that we have a certain
medical test to determine if person has this disease. The test produces a positive reading on 99.4% of those infected
with the disease. Suppose that this test gives a positive result in healthy patients 2% of the time. Assume we have 100,000 random individuals that follow the above information perfectly. a) Fill in the table.
Has Disease
Does Not Have Disease
Total
Test Positive
994
1980
2974
Test Negative
6
97020
97026
Total
1000
99000
100000
b) Determine
c) Determine 0.00006184
2. Suppose that it is known that a certain disease occurs in 4% of the population. Suppose also that we have a certain
medical test to determine if person has this disease. The test produces a positive reading on 99.4% of those infected
with the disease. Suppose that this test gives a positive result in healthy patients 2% of the time. Assume we have 100,000 random individuals that follow the above information perfectly. a) Fill in the table.
Has Disease
Does Not Have Disease
Total
Test Positive
3976
1920
5896
Test Negative
24
94080
94104
Total
4000
96000
100000
b) Determine
0.67435550
c) Determine 0.00025504
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