Giving a test to a group of students, the grades and gender are summarized below \begin{tabular}{|r|r|r|r|r|} \hline & A & B & C & Total \\ \hline Male & 11 & 14 & 7 & 32 \\ \hline Female & 2 & 20 & 3 & 25 \\ \hline Total & 13 & 34 & 10 & 57 \\ \hline \end{tabular} (Note: Round all answers to 4 decimal places where possible.) If one student is chosen at random, A. Find the probability that the student was female: B. Find the probability that the student was female and got a " $\mathrm{C}$ ": C. Find the probability that the student was female or got a "C": D. Find the probability that the student was female given they got a ' $C$ ':

Step 1 ：Given a test to a group of students, the grades and gender are summarized below: \begin{tabular}{|r|r|r|r|r|} \hline & A & B & C & Total \\ \hline Male & 11 & 14 & 7 & 32 \\ \hline Female & 2 & 20 & 3 & 25 \\ \hline Total & 13 & 34 & 10 & 57 \\ \hline \end{tabular}

Step 2 ：We are asked to find the following probabilities: A. The probability that the student was female. B. The probability that the student was female and got a 'C'. C. The probability that the student was female or got a 'C'. D. The probability that the student was female given they got a 'C'.

Step 3 ：The probability of an event is calculated by dividing the number of ways the event can occur by the total number of outcomes.

Step 4 ：For question A, the probability that the student was female is calculated by dividing the total number of female students by the total number of students. This gives us \(\frac{25}{57} = 0.4386\).

Step 5 ：For question B, the probability that the student was female and got a 'C' is calculated by dividing the number of female students who got a 'C' by the total number of students. This gives us \(\frac{3}{57} = 0.0526\).

Step 6 ：For question C, the probability that the student was female or got a 'C' is calculated by adding the probabilities of the two events and subtracting the probability of both events occurring. This gives us \(\frac{25}{57} + \frac{10}{57} - \frac{3}{57} = 0.5614\).

Step 7 ：For question D, the probability that the student was female given they got a 'C' is calculated by dividing the number of female students who got a 'C' by the total number of students who got a 'C'. This gives us \(\frac{3}{10} = 0.3\).

Step 8 ：Final Answer: A. The probability that the student was female is \(\boxed{0.4386}\). B. The probability that the student was female and got a 'C' is \(\boxed{0.0526}\). C. The probability that the student was female or got a 'C' is \(\boxed{0.5614}\). D. The probability that the student was female given they got a 'C' is \(\boxed{0.3}\).