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Question 1

A)Owen rolls a typical 6-sided number cube. List the outcomes for him rolling a prime number.(1 point)
Responses

{2,3,5}
left brace 2 comma 3 comma 5 right brace

{2,3}
left brace 2 comma 3 right brace

{4}
left brace 4 right brace

{1,3,5}
left brace 1 comma 3 comma 5 right brace
Question 2
A)
Maryn is doing a project on weather in different regions. She chooses two locations in the same state and compares their high temperatures over the next 10 days. Below are her findings.

Day 1 2 3 4 5 6 7 8 9 10
Location #1 70 78 72 67 61 70 72 73 78 77
Location #2 68 63 68 70 75 77 68 65 72 70
Describe what an intersection of the two events would look like as a subset.

(1 point)
Responses

{61,67,70,72,73,77,78}
left brace 61 comma 67 comma 70 comma 72 comma 73 comma 77 comma 78 right brace

{70,72,77}
left brace 70 comma 72 comma 77 right brace

{61,63,65,67,68,70,72,73,75,77,78}
left brace 61 comma 63 comma 65 comma 67 comma 68 comma 70 comma 72 comma 73 comma 75 comma 77 comma 78 right brace

{61,63,65,67,68,73,75,78}
left brace 61 comma 63 comma 65 comma 67 comma 68 comma 73 comma 75 comma 78 right brace
Question 3
A)A local farming club is selling raffle tickets for $15 each for a chance to win a milking cow. They will sell $6,000 worth of raffle tickets to fund their next project. If someone buys 2 tickets, what is the probability that that person will win the milking cow?(1 point)
Responses

1200
Start Fraction 1 over 200 End Fraction

30600
Start Fraction 30 over 600 End Fraction

360
Start Fraction 3 over 60 End Fraction

1400
Start Fraction 1 over 400 End Fraction
Question 4
A)What is the probability of rolling a sum greater than 10 and a sum of 10 when rolling two number cubes?(1 point)
Responses

13
Start Fraction 1 over 3 End Fraction

1144
Start Fraction 1 over 144 End Fraction

036
Start Fraction 0 over 36 End Fraction

336
Start Fraction 3 over 36 End Fraction
Question 5
A)The weather report says that in the following 60 days, 24 days will be cloudy, 15 days will be rainy, and 10 days will be cloudy and rainy. Let event A represent cloudy days and event B represent rainy days. Are the events A and B independent or dependent, and why?(1 point)
Responses

dependent, because P(A and B)≠P(A)⋅P(B)
dependent, because upper P left parenthesis upper A and upper B right parenthesis does not equal upper P left parenthesis upper A right parenthesis times upper P left parenthesis upper B right parenthesis

independent, because P(A and B)=P(A)⋅P(B)
independent, because upper P left parenthesis upper A and upper B right parenthesis equals upper P left parenthesis upper A right parenthesis times upper P left parenthesis upper B right parenthesis

dependent, because P(A)≠P(B)
dependent, because upper P left parenthesis upper A right parenthesis does not equal upper P left parenthesis upper B right parenthesis

dependent, because P(A)=P(B)
dependent, because upper P left parenthesis upper A right parenthesis equals upper P left parenthesis upper B right parenthesis
Question 6
A)Which of the following represents a dependent event?(1 point)
Responses

randomly picking a shirt from a drawer and replacing it because you want a different color
randomly picking a shirt from a drawer and replacing it because you want a different color

determining the reward for completing chores from a spinner that contains 6 different rewards and omitting the selected reward from the list once it has been selected
determining the reward for completing chores from a spinner that contains 6 different rewards and omitting the selected reward from the list once it has been selected

selecting a marker from a container of 18 markers, then replacing it and selecting another marker, repeating until you get the color that you desire
selecting a marker from a container of 18 markers, then replacing it and selecting another marker, repeating until you get the color that you desire

determining the reward for completing chores from a spinner that contains 6 different rewards and being able to get the same reward every time you spin
determining the reward for completing chores from a spinner that contains 6 different rewards and being able to get the same reward every time you spin
Question 7
A)Which of the following represents conditional probability?(1 point)
Responses

selecting a practice problem from a math book, given that it’s on an even numbered page
selecting a practice problem from a math book, given that it’s on an even numbered page

selecting a practice problem from a math book and recording whether the page number is even or odd
selecting a practice problem from a math book and recording whether the page number is even or odd

selecting a practice problem from a math book
selecting a practice problem from a math book

selecting a practice problem from a math book and also selecting a page to work from
selecting a practice problem from a math book and also selecting a page to work from
Question 8
A)
Use the table to answer the question.

Sport
Gender Baseball Basketball Football Soccer
Male 13 15 20 12
Female 23 16 13 21
A survey of favorite sports separates responses by gender. Answers are compiled in a two-way frequency table. Interpret the table to determine which sport is the most popular.

(1 point)
Responses

football
football

basketball
basketball

baseball
baseball

soccer
soccer
Question 9
A)
Use the table to answer the question.

Language

Grade French German Spanish Total
9th 58 47 63 168
10th 70 64 44 178
11th 67 57 65 189
Total 195 168 172 535
Students were surveyed about their current language class. Their responses are recorded in the table. If you were to choose a respondent from this survey at random, interpret the data in the table to determine the probability that the student chosen would be in the tenth grade. Round to the nearest whole number.

(1 point)
Responses

33%
33%

36%
36%

38%
38%

34%
34%
Question 10
A)
Use the table to answer the question.

Book Preference
Music Preference Likes Books Dislikes Books Total
Likes music 46 56 102
Dislikes music 68 30 98
Total 114 86 200
Let event A be a person who does not like books and event B be a person who likes music. Are the two events independent?

(1 point)
Responses

Yes, because P(A and B)=P(A)⋅P(B).
Yes, because upper P left parenthesis upper A and upper B right parenthesis equals upper P left parenthesis upper A right parenthesis times upper P left parenthesis upper B right parenthesis .

No, because P(A)≠P(B).
No, because upper P left parenthesis upper A right parenthesis does not equal upper P left parenthesis upper B right parenthesis .

Yes, because P(A and B)=56200.
Yes, because upper P left parenthesis upper A and upper B right parenthesis equals Start Fraction 56 over 200 End Fraction .

No, because P(A)=86200, P(B)=102200, and P(A and B)≠56200.

1 answer

Here are the answers to the questions provided:

Question 1

A) Owen rolls a typical 6-sided number cube. List the outcomes for him rolling a prime number.

  • Correct Response: {2,3,5}

Question 2

A) Describe what an intersection of the two events would look like as a subset.

  • Correct Response: {70,72,77}

Question 3

A) If someone buys 2 tickets, what is the probability that that person will win the milking cow?

  • Correct Response: Start Fraction 1 over 200 End Fraction

Question 4

A) What is the probability of rolling a sum greater than 10 and a sum of 10 when rolling two number cubes?

  • Correct Response: Start Fraction 3 over 36 End Fraction

Question 5

A) Are the events A and B independent or dependent, and why?

  • Correct Response: dependent, because P(A and B)≠P(A)⋅P(B)

Question 6

A) Which of the following represents a dependent event?

  • Correct Response: determining the reward for completing chores from a spinner that contains 6 different rewards and omitting the selected reward from the list once it has been selected

Question 7

A) Which of the following represents conditional probability?

  • Correct Response: selecting a practice problem from a math book, given that it’s on an even numbered page

Question 8

A) Interpret the table to determine which sport is the most popular.

  • Correct Response: football (since it has the highest total: 20 male + 13 female = 33)

Question 9

A) What is the probability that the student chosen would be in the tenth grade?

  • Total students = 535, Tenth grade students = 178, therefore the probability is: \[ \frac{178}{535} \approx 33% \]
  • Correct Response: 33%

Question 10

A) Are the two events independent?

  • Calculation:
    • P(A) = Number of people who dislike books = 98 / 200
    • P(B) = Number of people who like music = 102 / 200
    • P(A and B) = people who dislike books and like music = 68 / 200
    • Check if P(A and B) = P(A) * P(B)
    • Since \( P(A) \neq P(B) \) means they are dependent.
  • Correct Response: No, because P(A)≠P(B).

Feel free to review or ask about any specific question!