To solve the problem, we need to compute the conditional probability of a student receiving an "A" given that the student is female. The formula for conditional probability is:

$P(A \,|\, B) = \frac{P(A \cap B)}{P(B)}$

Here:

• $A$: The event that the student got an "A."
• $B$: The event that the student is female.

From the given table:

• The number of females who got an "A" ($A \cap B$) = 19.
• The total number of females ($B$) = 52.

So:

$P(\text{A | Female}) = \frac{\text{Number of females who got an "A"}}{\text{Total number of females}} = \frac{19}{52}.$

Thus, the probability is:

$P(\text{A | Female}) = \frac{19}{52} \approx 0.365 \, (\text{or } 36.5\%).$

Would you like a detailed breakdown of the formula or related concepts?

Related Questions:

1. What is the probability of a randomly chosen student being male and getting a "B"?
2. What is the probability of selecting a male student?
3. How do you calculate the probability of a student getting a "C" given they are female?
4. What is the total probability of a student scoring an "A" (regardless of gender)?
5. How does conditional probability differ from joint probability?

Tip:

To solve conditional probability problems, always start by identifying the subset of the population you're focusing on and ensure the denominator reflects that subset.