Posted: December 12th, 2022
4.3b hw conditional probability w/ tables
- A home pregnancy test was given to women, then pregnancy was verified through blood tests. The following table shows the home pregnancy test results.
Positive
Negative
Total
Pregnant
69
4
73
Not Pregnant
9
51
60
Total
78
55
133
Round your answers to the nearest thousandth.
PP (positive) ∣
pregnant) =
PP(pregnant)
positive) =
PP
(negative)
pregnant) =
PP(not pregnant)
negative) =
2. A test was given to a group of students. The grades and gender are summarized below
A
B
C
Total
Male
4
15
16
35
Female
7
12
14
33
Total
11
27
30
68
If one student is chosen at random from those who took the test,
Find the probability that the student was female GIVEN they got an ‘A’.
____________________________________________________
3. Giving a test to a group of students, the grades and gender are summarized below
A
B
C
Total
Male
10
7
9
26
Female
5
17
19
41
Total
15
24
28
67
If one student is chosen at random,
Find the probability that the student was male: ______
Find the probability that the student was male AND got a “C”: ___________
Find the probability that the student was male OR got an “C”: ___________
If one student is chosen at random, find the probability that the student got a ‘B’ GIVEN they are female: _____________
4. Giving a test to a group of students, the grades and gender are summarized below
A
B
C
Total
Male
6
9
3
18
Female
10
2
15
27
Total
16
11
18
45
If one student is chosen at random,
- Find the probability that the student was male: _________
- Find the probability that the student was male AND got a “C”: ______
- Find the probability that the student was male OR got a “C”: ______
- If one student is chosen at random, find the probability that the student was male GIVEN they got a ‘C’: ____________
5. Giving a test to a group of students, the grades and gender are summarized below
A
B
C
Total
Male
18
12
16
46
Female
8
3
13
24
Total
26
15
29
70
If one student is chosen at random,
Find the probability that the student was female:
Find the probability that the student was male AND got a “B”:
Find the probability that the student was female OR got an “C”:
If one student is chosen at random, find the probability that the student got a ‘A’ GIVEN they are female:
6. Giving a test to a group of students, the grades and gender are summarized below
A
B
C
Total
Male
12
13
8
33
Female
19
2
20
41
Total
31
15
28
74
If one student is chosen at random,
Find the probability that the student was female AND got a “A”.
7. A CBS News poll conducted June 10 and 11, 2006, among a nationwide random sample of 651 adults, asked those adults about their party affiliation (Democrat, Republican or none) and their opinion of how the US economy was changing (“getting better,” “getting worse” or “about the same”). The results are shown in the table below.
better
same
worse
Republican
38
104
44
Democrat
12
87
137
none
21
90
118
Express each of your answers as a percent rounded to the nearest tenth (for example, 12.3%).
- What percent of survey respondents identified themselves as affiliated with neither party (marginal probability)?
% - What percent of survey respondents thought the economy was about the same and were affiliated with neither party (joint probability)?
% - What percent of those affiliated with neither party thought the economy was about the same (conditional probability)?
%
8. Giving a test to a group of students, the grades and gender are summarized below
A
B
C
Total
Male
5
13
16
34
Female
19
14
18
51
Total
24
27
34
85
If one student is chosen at random,
Find the probability that the student got a ‘B’ GIVEN they are female.
9. Giving a test to a group of students, the grades and gender are summarized below
A
B
C
Total
Male
11
4
5
20
Female
16
8
13
37
Total
27
12
18
57
If one student is chosen at random,
Find the probability that the student was female OR got an “B”.
10. Four hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.
18–24
25–34
35–55
55 and over
Total
Liked Crunchicles
1
5
6
12
24
Disliked Crunchicles
13
13
11
14
51
No Preference
76
94
45
110
325
Total
90
112
62
136
400
One consumer from the survey is selected at random. Use reduced fractions for your responses to each of the following questions.
What is the probability that the consumer is 18–24 years of age, given that he/she dislikes Crunchicles?
What is the probability that the selected consumer dislikes Crunchicles?
What is the probability that the selected consumer is 35–55 years old or likes Crunchicles?
If the selected consumer is 70 years old, what is the probability that he/she likes Crunchicles?
11. A CBS News poll conducted June 10 and 11, 2006, among a nationwide random sample of 651 adults, asked those adults about their party affiliation (Democrat, Republican or none) and their opinion of how the US economy was changing (“getting better,” “getting worse” or “about the same”). The results are shown in the table below.
better
same
worse
Republican
38
104
44
Democrat
12
87
137
none
21
90
118
Express your answers as a decimal and round to the nearest 0.001 (in other words, type 0.123, not 12.3% or 0.123456).
If we randomly select one of the adults who participated in this study, compute:
P(Republican) =
P(better) =
P(better|Republican) =
P(Republican|better) =
P(Republican and better) =
12. A test was given to a group of students. The grades and gender are summarized below
A
B
C
Total
Male
15
6
10
31
Female
13
20
12
45
Total
28
26
22
76
If one student is chosen at random from those who took the test,
Find the probability that the student got a ‘B’ GIVEN they are female.
13. A jar contains 8 red marbles, numbered 1 to 8, and 11 blue marbles numbered 1 to 11.
a) A marble is chosen at random. If you’re told the marble is red, what is the probability that it has the number 5 on it?
b) The first marble is replaced, and another marble is chosen at random. If you’re told the marble has the number 1 on it, what is the probability the marble is red?
15.
A poll has taken of 13,833 working adults aged 40-70 to determine their level of education. The participants were classified by sex and by level of education. The results are shown below.
Education Level
Male
Female
Total
High School or Less
3755
2634
6389
Bachelor’s Degree
3264
3106
6370
Master’s Degree
473
464
937
Ph.D.
69
68
137
Total
7561
6272
13,833
A person is selected at random. Compute the following probabilities.
(a) What is the probability that the selected person is male, given that he has a Master’s degree?
(b) What is the probability that the selected person does not have a Master’s degree, given that he is male?
(c) What is the probability that the selected person is female, given that she has a Bachelor’s degree?
(d) What is the probability that the selected person has a Ph.D., given that she is female?
17. A bag of M&M’s has 4 red, 6 green, 2 blue, and 5 yellow M&M’s. Suppose you randomly select two M&M’s from the bag one at a time without replacing the first M&M.
Let A = first M&M is blue and B = second M&M is blue.
Find the following probabilities. (Write your answers as fractions.)
a) P(A) =
b) P(B | A) =
c) P(A and B) =
18. A bag of M&M’s has 3 red, 4 green, 6 blue, and 2 yellow M&M’s. Suppose you randomly select two M&M’s from the bag one at a time while replacing the first M&M.
Let A = first M&M is green and B = second M&M is green.
Find the following probabilities. (Write your answers as fractions.)
a) P(A) =
b) P(B | A) =
c) P(A and B) =
19. Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 22 of the 62 boxes on the shelf have the secret decoder ring. The other 40 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring?
Probability =
(Please enter a reduced fraction)
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