6. c. Determine P(B1 and A2). (Round your answer to 2 decimal places.)
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6. c. Determine P(B1 and A2). (Round your answer to 2 decimal places.)
![### Probability Table and Calculations
#### Refer to the following table.
| Second Event | First Event | Total |
|--------------|-------------|-------|
| | A₁ | A₂ | A₃ | |
| B₁ | 5 | 8 | 14 | 27 |
| B₂ | 8 | 23 | 9 | 40 |
| **Total** | 13 | 31 | 23 | 67 |
- **Click here for the Excel Data File:** [Excel Data File]
---
#### a. Determine \( P(A₃) \). *(Round your answer to 2 decimal places.)*
\[ P(A₃) = \frac{23}{67} \approx \]
\[ \boxed{\phantom{00}} \]
---
#### b. Determine \( P(A₁ | B₁) \). *(Round your answer to 2 decimal places.)*
\[ P(A₁ | B₁) = \frac{5}{27} \approx \]
\[ \boxed{\phantom{00}} \]
---
The table presented is a contingency table that shows the distribution of two categorical variables: "First Event" and "Second Event." It contains the joint frequencies for combinations of these events (e.g., the frequency of \( A_1 \) occurring with \( B_1 \)).
The row labeled "Total" provides the marginal frequencies for each category of the "First Event." Similarly, the column labeled "Total" offers the marginal frequencies for each category of the "Second Event." The bottom-right cell gives the grand total, which is the sum of all joint frequencies.
This table can be used to calculate various probabilities, as illustrated in the example problems (a) and (b).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55f0052a-9d0d-41a8-9339-203ce40e3605%2F9ab512a3-7852-4055-a8c3-6bfe442042ad%2Frnv9ym_processed.png&w=3840&q=75)
Transcribed Image Text:### Probability Table and Calculations
#### Refer to the following table.
| Second Event | First Event | Total |
|--------------|-------------|-------|
| | A₁ | A₂ | A₃ | |
| B₁ | 5 | 8 | 14 | 27 |
| B₂ | 8 | 23 | 9 | 40 |
| **Total** | 13 | 31 | 23 | 67 |
- **Click here for the Excel Data File:** [Excel Data File]
---
#### a. Determine \( P(A₃) \). *(Round your answer to 2 decimal places.)*
\[ P(A₃) = \frac{23}{67} \approx \]
\[ \boxed{\phantom{00}} \]
---
#### b. Determine \( P(A₁ | B₁) \). *(Round your answer to 2 decimal places.)*
\[ P(A₁ | B₁) = \frac{5}{27} \approx \]
\[ \boxed{\phantom{00}} \]
---
The table presented is a contingency table that shows the distribution of two categorical variables: "First Event" and "Second Event." It contains the joint frequencies for combinations of these events (e.g., the frequency of \( A_1 \) occurring with \( B_1 \)).
The row labeled "Total" provides the marginal frequencies for each category of the "First Event." Similarly, the column labeled "Total" offers the marginal frequencies for each category of the "Second Event." The bottom-right cell gives the grand total, which is the sum of all joint frequencies.
This table can be used to calculate various probabilities, as illustrated in the example problems (a) and (b).
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