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.