The question asks to calculate the probability that a student is male given that they received a grade of C. This involves conditional probability.

From the table provided:

• Total number of students who received a grade of C: 22
• Number of males who received a grade of C: 16
• Conditional probability formula:
  $P(\text{Male | Grade C}) = \frac{\text{Number of males with grade C}}{\text{Total number of students with grade C}}$

Substitute the values:
$P(\text{Male | Grade C}) = \frac{16}{22} = \frac{8}{11}$

Final Answer:

The probability that the student is male, given they got a C, is:
$\boxed{\frac{8}{11}}$

Would you like further details on how conditional probability works, or have any additional questions?

Related Questions:

1. What is the probability that a student chosen at random is female and got a grade of A?
2. How do you calculate $P(\text{Female | Grade B})$?
3. What is the probability of randomly selecting a student who received a grade of A?
4. Can you explain the difference between joint and conditional probabilities?
5. How would the result change if the total number of students was different but proportions stayed the same?

Tip:

When working with conditional probabilities, always ensure that the "given" condition's total serves as the denominator!