Use the Data Given Below to Answer the Following Questions)

Multiple Choice

Use the data given below to answer the following questions) .
15 students were asked to choose between the broad categories of Arts, Science, and Math as their preferred area of study. $\begin{array} { | c | c | c | } \hline \text { Respondent } & \text { Gender } & \text { Preference } \\\hline 1 & \text { Fernale } & \text { Arts } \\\hline 2 & \text { Male } & \text { Science } \\\hline 3 & \text { Male } & \text { Math } \\\hline 4 & \text { Fernale } & \text { Arts } \\\hline 5 & \text { Fernale } & \text { Math } \\\hline 6 & \text { Male } & \text { Science } \\\hline 7 & \text { Male } & \text { Math } \\\hline 8 & \text { Male } & \text { Math } \\\hline 9 & \text { Fernale } & \text { Arts } \\\hline 10 & \text { Male } & \text { Arts } \\\hline 11 & \text { Male } & \text { Science } \\\hline 12 & \text { Fernale } & \text { Science } \\\hline 13 & \text { Fernale } & \text { Math } \\\hline 14 & \text { Male } & \text { Arts } \\\hline 15 & \text { Fernale } & \text { Arts }\\\hline \end{array}$
-Which of the following will hold true if events X and Y are independent?

A) PX) = PY) × PX and Y)
B) PY) = PX|Y)
C) PX and Y) = [PX) + PY) ] - PX or Y)
D) PX) = PX|Y)