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Let's work through the probability questions from the table in your image.

### Given table:
|         | A   | B   | C   | Total |
|---------|-----|-----|-----|-------|
| Male    | 4   | 20  | 8   | 32    |
| Female  | 13  | 5   | 7   | 25    |
| **Total**| 17  | 25  | 15  | 57    |

### We will solve each question one by one:

#### A. Find the probability that the student was female.
The total number of students is 57. The number of females is 25. 

\[
P(\text{female}) = \frac{\text{Number of females}}{\text{Total students}} = \frac{25}{57} \approx 0.4386 \quad \text{(or 43.86%)}.
\]

Your input of **26.50%** seems to have been incorrect.

#### B. Find the probability that the student was female **and** got an "A."
The number of females who got an "A" is 13. The total number of students is 57.

\[
P(\text{female AND A}) = \frac{\text{Number of females who got an A}}{\text{Total students}} = \frac{13}{57} \approx 0.2281 \quad \text{(or 22.81%)}.
\]

Your input of **18.39%** was incorrect as well.

#### C. Find the probability that the student was female **or** got an "A."
To calculate the probability of **female OR A**, we apply the inclusion-exclusion principle:

\[
P(\text{female OR A}) = P(\text{female}) + P(\text{A}) - P(\text{female AND A}).
\]

- \( P(\text{female}) = \frac{25}{57} \approx 0.4386 \),
- \( P(\text{A}) = \frac{17}{57} \approx 0.2982 \),
- \( P(\text{female AND A}) = \frac{13}{57} \approx 0.2281 \).

Now, substitute these into the formula:

\[
P(\text{female OR A}) = 0.4386 + 0.2982 - 0.2281 = 0.5087 \quad \text{(or 50.87%)}.
\]

#### D. If one student is chosen at random, find the probability that the student was female **given** they got an "A."
This is a conditional probability question:

\[
P(\text{female | A}) = \frac{P(\text{female AND A})}{P(\text{A})}.
\]

From earlier, we know:
- \( P(\text{female AND A}) = \frac{13}{57} \approx 0.2281 \),
- \( P(\text{A}) = \frac{17}{57} \approx 0.2982 \).

Now calculate the conditional probability:

\[
P(\text{female | A}) = \frac{0.2281}{0.2982} \approx 0.7651 \quad \text{(or 76.51%)}.
\]

Your input of **76.47%** was very close!

---

Would you like more details on any of the calculations? Here are 5 follow-up questions to deepen your understanding:

1. How does the inclusion-exclusion principle work in probability?
2. What is the difference between conditional and joint probability?
3. Can you apply these concepts to a different set of data?
4. How would the results change if more students were added to the dataset?
5. Why is it important to use total numbers in probability questions like these?

**Tip:** Always double-check probabilities to ensure they add up logically—this can prevent calculation errors!

Find the probability that a student was female, the probability of being female and getting an A, and other related conditional probabilities based on a table of student grades and gender.

Solve a detailed probability problem involving student grades and gender. Learn how to calculate probabilities, including joint and conditional probabilities, using the inclusion-exclusion principle. Suitable for high school students.

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