1. **Problem Statement:** Given the table of grades by gender, we need to find various probabilities related to the students. 2. **Total number of students:** $$74$$ (given in the table). 3. **(a) Probability the student was male:** $$P(\text{Male}) = \frac{\text{Number of males}}{\text{Total students}} = \frac{20}{74}$$ 4. **(b) Probability the student did NOT get a "C":** Number of students who got "C" = 28 So, number who did NOT get "C" = $$74 - 28 = 46$$ $$P(\text{Not C}) = \frac{46}{74}$$ 5. **(c) Probability the student was female AND got a "C":** Number of females who got "C" = 19 $$P(\text{Female and C}) = \frac{19}{74}$$ 6. **(d) Probability the student was male GIVEN they got a "B":** Number of students who got "B" = 25 Number of males who got "B" = 5 Conditional probability formula: $$P(\text{Male} | B) = \frac{P(\text{Male and B})}{P(B)} = \frac{5/74}{25/74} = \frac{5}{25} = \frac{1}{5}$$ 7. **(e) Probability the student got a "C" GIVEN they are female:** Number of females = 54 Number of females who got "C" = 19 $$P(C | \text{Female}) = \frac{19}{54}$$ **Final answers:** (a) $$\frac{20}{74} \approx 0.2703$$ (b) $$\frac{46}{74} \approx 0.6216$$ (c) $$\frac{19}{74} \approx 0.2568$$ (d) $$\frac{1}{5} = 0.2$$ (e) $$\frac{19}{54} \approx 0.3519$$