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

1 answer

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 \(0.5789\).