Undergraduate Major Business Engineering Other Totals Full Time Part Time Totals 420 399 819 394 592 986 75 46 121 889 1037 1926 Develop a joint probability table for these data in the blue cells Place your values in the green cells (to 3 decimals) Part A: Formulas Used Part A: Joint Probability Table Business Engineering Other Totals Full Time Part Time Totals Full Time Part Time Totals Business #N/A Engineering #N/A Other #N/A #AIA Totals #N/A Part C: Part D: Question Prompts for Parts C & D Part Clf a student intends to attend clases full - time in pursuit of an MBA degree, what is the probability that the student was an undergraduate Engineering major (to 3 decimals)? Part D Part C: Part D: If a student was an undergraduate Business major, what is the probability that the student intends to attend classes full - time in pursuit of an MBA degree (to 3 decimals)?
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Undergraduate Major Business Engineering Other Totals Full Time Part Time Totals 420 399 819 394 592 986 75 46 121 889 1037 1926 Develop a joint probability table for these data in the blue cells Place your values in the green cells (to 3 decimals) Part A: Formulas Used Part A: Joint Probability Table Business Engineering Other Totals Full Time Part Time Totals Full Time Part Time Totals Business #N/A Engineering #N/A Other #N/A #AIA Totals #N/A Part C: Part D: Question Prompts for Parts C & D Part Clf a student intends to attend clases full - time in pursuit of an MBA degree, what is the probability that the student was an undergraduate Engineering major (to 3 decimals)? Part D Part C: Part D: If a student was an undergraduate Business major, what is the probability that the student intends to attend classes full - time in pursuit of an MBA degree (to 3 decimals)?
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Asked by: suni
Created at: 2025-09-16 08:54:35
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# Joint Probability Table for MBA Students
Given data (cross-tabulated):
| Undergraduate Major | Full Time | Part Time | Total |
|---------------------|-----------|-----------|-------|
| Business | 420 | 399 | 819 |
| Engineering | 394 | 592 | 986 |
| Other | 75 | 46 | 121 |
| **Totals** | 889 | 1037 | 1926 |
---
## Part A: Formulas Used
- **Joint Probability:**
\( P(A \cap B) = \frac{\text{Number in both A and B}}{\text{Total number}} \)
- **Conditional Probability:**
\( P(A | B) = \frac{P(A \cap B)}{P(B)} \)
---
## Part B: Joint Probability Table
Calculated as:
\( \text{Probability} = \frac{\text{Cell Count}}{1926} \)
| Undergraduate Major | Full Time | Part Time | Total |
|---------------------|-------------|-------------|------------|
| Business | 0.218 | 0.207 | 0.425 |
| Engineering | 0.205 | 0.307 | 0.512 |
| Other | 0.039 | 0.024 | 0.063 |
| **Total** | 0.462 | 0.538 | 1.000 |
**Green Cells:** (rounded to three decimals, as required)
---
## Part C: Probability (Engineering major | Full-Time MBA)
- **Formula:**
\( P(\text{Engineering} | \text{Full Time}) = \frac{P(\text{Engineering} \cap \text{Full Time})}{P(\text{Full Time})} \)
- **Calculation:**
\( P = \frac{394/1926}{889/1926} = \frac{394}{889} \approx 0.443 \)
**Answer:**
**0.443**
---
## Part D: Probability (Full-Time MBA | Business major)
- **Formula:**
\( P(\text{Full Time} | \text{Business}) = \frac{P(\text{Business} \cap \text{Full Time})}{P(\text{Business})} \)
- **Calculation:**
\( P = \frac{420/1926}{819/1926} = \frac{420}{819} \approx 0.513 \)
**Answer:**
**0.513**
---
## Summary Table
| Question | Probability |
|------------------------------|-------------|
| Engineering | Full Time | 0.443 |
| Full Time | Business Major | 0.513 |
---
## Notes
- All probabilities rounded to three decimals.
- Total students = **1926**.
- Each cell in the joint table = count / 1926.
---
### Alt Text
_No images provided; if a table is shown, alt text could be: "Table showing joint probabilities for undergraduate major and MBA attendance status."_
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