Question
Two-Way Tables Discussion
Create your own frequency table by using the table shown. Choose two categories to compare in the top row and two categories to compare in the first column (Refer to the tables in the lesson as a reference). Include a title for your table. Ensure that each row and column adds to the corresponding totals at the end of each row and column. Answer 1-4 and in your discussion post and leave number 5 blank for your peers to respond to.
Two-Way Tables
Table Title
Category Category Total
Category
Category
Total
Let event A be _____.
Find P(A).
Let event B be _____.
Find P(B).
Determine if the events are independent by using P(A and B) = P(A) * P(B) to justify your answer. (Leave this one blank for your peers to respond to in the discussion post.)
Post a detailed response to the Independent Events in Two-way tables prompt. Then respond to two classmates' posts.
Select the link to access the Two-Way Tables Discussion.
Create your own frequency table by using the table shown. Choose two categories to compare in the top row and two categories to compare in the first column (Refer to the tables in the lesson as a reference). Include a title for your table. Ensure that each row and column adds to the corresponding totals at the end of each row and column. Answer 1-4 and in your discussion post and leave number 5 blank for your peers to respond to.
Two-Way Tables
Table Title
Category Category Total
Category
Category
Total
Let event A be _____.
Find P(A).
Let event B be _____.
Find P(B).
Determine if the events are independent by using P(A and B) = P(A) * P(B) to justify your answer. (Leave this one blank for your peers to respond to in the discussion post.)
Post a detailed response to the Independent Events in Two-way tables prompt. Then respond to two classmates' posts.
Select the link to access the Two-Way Tables Discussion.
Answers
GPT-4o mini
## Two-Way Table Title: "Favorite Fruit and Day of the Week Preferences"
| | Monday | Tuesday | Wednesday | Total |
|---------------|--------|---------|-----------|-------|
| Apples | 10 | 12 | 8 | 30 |
| Bananas | 14 | 9 | 16 | 39 |
| Oranges | 8 | 11 | 6 | 25 |
| Total | 32 | 32 | 30 | 94 |
### Event Definitions:
Let event A be "Choosing someone who prefers Apples."
Let event B be "Choosing someone who prefers Bananas."
### Probability Calculations:
1. **Find P(A):**
- The total number of people surveyed is 94 (total from the table).
- The total who prefer Apples is 30.
- Thus, \( P(A) = \frac{30}{94} \approx 0.319 \).
2. **Find P(B):**
- The total who prefer Bananas is 39.
- Thus, \( P(B) = \frac{39}{94} \approx 0.415 \).
3. **Determine if the events are independent:**
- First, calculate \( P(A \, \text{and} \, B) \). In this case, since a single person cannot prefer both fruits simultaneously, \( P(A \, \text{and} \, B) = 0 \).
- Now, check if \( P(A) * P(B) \):
- \( P(A) * P(B) = \left(\frac{30}{94}\right) * \left(\frac{39}{94}\right) \approx 0.132 \).
- Since \( P(A \, \text{and} \, B) \neq P(A) * P(B) \) (0 does not equal approximately 0.132), events A and B are not independent.
4. **Conclusion about independence:**
- Based on this information, we can conclude that the preference for Apples and Bananas among survey respondents are not independent events.
5. **(Leave this blank for peers to respond)**
| | Monday | Tuesday | Wednesday | Total |
|---------------|--------|---------|-----------|-------|
| Apples | 10 | 12 | 8 | 30 |
| Bananas | 14 | 9 | 16 | 39 |
| Oranges | 8 | 11 | 6 | 25 |
| Total | 32 | 32 | 30 | 94 |
### Event Definitions:
Let event A be "Choosing someone who prefers Apples."
Let event B be "Choosing someone who prefers Bananas."
### Probability Calculations:
1. **Find P(A):**
- The total number of people surveyed is 94 (total from the table).
- The total who prefer Apples is 30.
- Thus, \( P(A) = \frac{30}{94} \approx 0.319 \).
2. **Find P(B):**
- The total who prefer Bananas is 39.
- Thus, \( P(B) = \frac{39}{94} \approx 0.415 \).
3. **Determine if the events are independent:**
- First, calculate \( P(A \, \text{and} \, B) \). In this case, since a single person cannot prefer both fruits simultaneously, \( P(A \, \text{and} \, B) = 0 \).
- Now, check if \( P(A) * P(B) \):
- \( P(A) * P(B) = \left(\frac{30}{94}\right) * \left(\frac{39}{94}\right) \approx 0.132 \).
- Since \( P(A \, \text{and} \, B) \neq P(A) * P(B) \) (0 does not equal approximately 0.132), events A and B are not independent.
4. **Conclusion about independence:**
- Based on this information, we can conclude that the preference for Apples and Bananas among survey respondents are not independent events.
5. **(Leave this blank for peers to respond)**