Giving a test to a group of students, the table below summarizes the grade earned by gender.

A	B	C	Total
Male	8	15	10	33
Female	17	16	4	37
Total	25	31	14	70

If one student is chosen at random, find the probability that the student earned grade A given the student is female. Round your answer to four decimal places.

To find the probability that a student earned grade A given the student is female, we need to apply the formula for conditional probability:

\[
P(A | \text{Female}) = \frac{P(A \cap \text{Female})}{P(\text{Female})}
\]

### Step-by-Step Solution:

1. **Total number of female students**: From the table, we know there are 37 female students.

2. **Number of female students who earned grade A**: There are 17 female students who earned grade A.

3. **Conditional probability**: The probability of selecting a student who earned grade A, given that the student is female, is the ratio of the number of female students who earned grade A to the total number of female students.

\[
P(A | \text{Female}) = \frac{17}{37}
\]

4. **Calculate the probability**:

\[
P(A | \text{Female}) = \frac{17}{37} \approx 0.4595
\]

### Final Answer:

\[
P(A | \text{Female}) \approx 0.4595
\]

Would you like further clarification or more details on this solution?

### Related Questions:
1. What is the probability that a randomly chosen student is male and earned grade B?
2. What is the probability that a student chosen at random earned grade C?
3. What is the probability that a student is female given that the student earned grade B?
4. What is the overall probability of selecting a student who earned grade A?
5. What is the probability of selecting a male student given the student earned grade C?

### Tip: 
When dealing with conditional probabilities, always focus on the subset of the given condition first, then calculate based on the relevant total within that subset.

If one student is chosen at random, find the probability that the student earned grade A given the student is female. Round your answer to four decimal places.

Learn how to calculate the conditional probability that a student earned grade A given they are female. Using data from a group of students and the conditional probability formula, this step-by-step guide is ideal for high school students. The final answer is approximately 0.4595.

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