4.3b hw conditional probability w/ tables

  1. 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,

  1. Find the probability that the student was male: _________
  2. Find the probability that the student was male AND got a “C”: ______
  3. Find the probability that the student was male OR got a “C”: ______
  4. 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%).

  1. What percent of survey respondents identified themselves as affiliated with neither party (marginal probability)?
    %
  2. What percent of survey respondents thought the economy was about the same and were affiliated with neither party  (joint probability)?
    %
  3. 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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