Question

In a class of students, the following data table summarizes the gender of the students and whether they have an A in the class. What is the probability that a student is a male given that they have an A?
Female Male
Has an A 8 11
Does not have an A 7 2
Answer

Answer 1

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 \(0.5789\).