Question
Thomas is rolling a fair six-sided number cube numbered from 1 to 6. The situation with a probability closest or equal to 0 is ___________________. * Rolling a number greater than 1 Rolling a 1 Rolling a number less than 1 Rolling a odd number For a class activity, each student randomly chooses a number from 1 to 10. Which model shows the probability of a student choosing a multiple of 4? * 2/8 2/10 8/2 10/2 A bag contains 4 white, 3 blue, and 3 red marbles. Find the probability of choosing a red marble, then a white marble if the marbles are replaced. * 7/10 7/100 12/90 12/100 Find the probability of spinning P(not 7) * 1/7 1/8 7/8 4/8 Sonya is thinking of conducting a survey with her seventh-grade classmates. She knows she will need to use a sample of students in her survey. Which of the following surveys would not be valid with a sample of seventh-grade classmates? * theme for the seventh-grade Fun Night bank that offers the most services milk choices offered at lunch best backpack for school
Answers
GPT-4o mini
Let's address each question one by one:
1. **Probability closest or equal to 0**:
- Rolling a number greater than 1 (possible outcomes: 2, 3, 4, 5, 6) - Probability = 5/6
- Rolling a 1 (only 1 outcome) - Probability = 1/6
- Rolling a number less than 1 (impossible outcome) - Probability = 0
- Rolling an odd number (possible outcomes: 1, 3, 5) - Probability = 3/6 = 1/2
- The situation with a probability closest or equal to 0 is **Rolling a number less than 1**.
2. **Probability of choosing a multiple of 4 from 1 to 10**:
- The multiples of 4 between 1 and 10 are: 4, 8 (total = 2 outcomes)
- Total possible outcomes = 10
- Probability = 2/10 (simplified = 1/5)
- The model that shows the probability of a student choosing a multiple of 4 is **2/10**.
3. **Probability of choosing a red marble, then a white marble if the marbles are replaced**:
- Total marbles = 4 (white) + 3 (blue) + 3 (red) = 10
- Probability of choosing a red marble = 3/10
- Since the marble is replaced, the total stays 10.
- Probability of choosing a white marble = 4/10
- Combined probability = (3/10) * (4/10) = 12/100
- The probability is **12/100**.
4. **Probability of spinning P(not 7)**:
- Assuming a standard spinner with 8 equal sections numbered 1 to 8, only 1 section (the section with 7) does not meet the criteria of "not 7."
- Probability of not spinning a 7 = (Total outcomes - Outcomes with 7) / Total outcomes = (8 - 1)/8 = 7/8
- The probability of spinning P(not 7) is **7/8**.
5. **Survey validity**:
- The context requires a topic that could apply specifically to seventh-grade students.
- “Theme for the seventh-grade Fun Night” would be relevant to seventh graders.
- "Best backpack for school" can apply to seventh graders but isn't specific to them considering other grades.
- "Bank that offers the most services" likely addresses a broader demographic and may not be relevant to seventh graders.
- "Milk choices offered at lunch" is also relevant since lunch options are standard across grades.
- **The survey topic that would not be valid with a sample of seventh-grade classmates would be "bank that offers the most services."**
I hope this helps clarify the solutions to your questions!
1. **Probability closest or equal to 0**:
- Rolling a number greater than 1 (possible outcomes: 2, 3, 4, 5, 6) - Probability = 5/6
- Rolling a 1 (only 1 outcome) - Probability = 1/6
- Rolling a number less than 1 (impossible outcome) - Probability = 0
- Rolling an odd number (possible outcomes: 1, 3, 5) - Probability = 3/6 = 1/2
- The situation with a probability closest or equal to 0 is **Rolling a number less than 1**.
2. **Probability of choosing a multiple of 4 from 1 to 10**:
- The multiples of 4 between 1 and 10 are: 4, 8 (total = 2 outcomes)
- Total possible outcomes = 10
- Probability = 2/10 (simplified = 1/5)
- The model that shows the probability of a student choosing a multiple of 4 is **2/10**.
3. **Probability of choosing a red marble, then a white marble if the marbles are replaced**:
- Total marbles = 4 (white) + 3 (blue) + 3 (red) = 10
- Probability of choosing a red marble = 3/10
- Since the marble is replaced, the total stays 10.
- Probability of choosing a white marble = 4/10
- Combined probability = (3/10) * (4/10) = 12/100
- The probability is **12/100**.
4. **Probability of spinning P(not 7)**:
- Assuming a standard spinner with 8 equal sections numbered 1 to 8, only 1 section (the section with 7) does not meet the criteria of "not 7."
- Probability of not spinning a 7 = (Total outcomes - Outcomes with 7) / Total outcomes = (8 - 1)/8 = 7/8
- The probability of spinning P(not 7) is **7/8**.
5. **Survey validity**:
- The context requires a topic that could apply specifically to seventh-grade students.
- “Theme for the seventh-grade Fun Night” would be relevant to seventh graders.
- "Best backpack for school" can apply to seventh graders but isn't specific to them considering other grades.
- "Bank that offers the most services" likely addresses a broader demographic and may not be relevant to seventh graders.
- "Milk choices offered at lunch" is also relevant since lunch options are standard across grades.
- **The survey topic that would not be valid with a sample of seventh-grade classmates would be "bank that offers the most services."**
I hope this helps clarify the solutions to your questions!