To find the probability that a student is male given that they have an A, we can use the formula for conditional probability:
\[ P(\text{Male} | \text{Has an A}) = \frac{P(\text{Male and Has an A})}{P(\text{Has an A})} \]
From the data provided, we have:
- Number of males with an A = 11
- Number of females with an A = 8
To find \(P(\text{Has an A})\), we need to calculate the total number of students who have an A:
\[ \text{Total Has an A} = \text{Number of Males with A} + \text{Number of Females with A} = 11 + 8 = 19 \]
Then, to find \(P(\text{Male and Has an A})\), we use the number of males who have an A, which is 11.
Now we can calculate the conditional probability:
\[ P(\text{Male} | \text{Has an A}) = \frac{11}{19} \]
Thus, the probability that a student is male given that they have an A is:
\[ \frac{11}{19} \approx 0.5789 \]
So, the final answer is:
\(\frac{11}{19}\) or approximately \(0.5789\).