We are asked to find the probability that the student was male, given that they received an "A". This is a conditional probability problem, where we need to find:

$P(\text{Male} \mid A)$

The formula for conditional probability is:

$P(\text{Male} \mid A) = \frac{P(\text{Male} \cap A)}{P(A)}$

Step 1: Determine $P(\text{Male} \cap A)$

From the table, the number of males who received an "A" is 18. Since the total number of students is 61, we have:

$P(\text{Male} \cap A) = \frac{18}{61}$

Step 2: Determine $P(A)$

The total number of students who received an "A" is 25 (both male and female), so:

$P(A) = \frac{25}{61}$

Step 3: Calculate $P(\text{Male} \mid A)$

Now, applying the formula for conditional probability:

$P(\text{Male} \mid A) = \frac{\frac{18}{61}}{\frac{25}{61}} = \frac{18}{25}$

Thus, the probability that the student was male, given they received an "A", is:

$P(\text{Male} \mid A) = \frac{18}{25} = 0.72$

The probability is $0.72$, or 72%.

Would you like further details or clarifications on this?

Related Questions:

1. What is the probability that a randomly chosen student is female given that they got an "A"?
2. What is the probability that a randomly chosen student received a "B"?
3. What is the probability that a randomly chosen student is male?
4. What is the total probability that a randomly chosen student received a "C"?
5. What is the probability that a student is female given they got a "B"?

Tip:

For conditional probability, always start by identifying the subset of interest (in this case, students who received an "A") and then calculate the proportion for the desired condition within that subset.