One hundred upper division students attending a career fair at a university were categorized according to class and according to primary career motivation. The table shows the results. If one of these students is to be selected at random, find the probability that the student selected is a junior, given that their primary motivation is a sense of giving to society. \begin{tabular}{l|c|c|c|c|} \hline \multirow{2}{*}{} & \multicolumn{3}{|c|}{ Primary Career Motivation } & \multirow{2}{*}{. } \\ \cline { 2 - 4 } & Money & \begin{tabular}{c} Allowed to be \\ Creative \end{tabular} & \begin{tabular}{c} Sense of \\ Giving to \\ Society \end{tabular} & Total \\ \hline Junior & 16 & 13 & 12 & 41 \\ Senior & 8 & 8 & 43 & 59 \\ \hline Total & 24 & 21 & 55 & 100 \\ \hline \end{tabular} The probability that the student selected is a junior, given that the primary motivation is a sense of giving to society is (Simplify your answer. Type an integer or a fraction.)
Solution
Step 1 ：Given a table of one hundred upper division students attending a career fair at a university, categorized according to class and primary career motivation.
Step 2 ：We are asked to find the probability that a randomly selected student is a junior, given that their primary motivation is a sense of giving to society.
Step 3 ：From the table, we can see that the number of juniors whose primary motivation is a sense of giving to society is 12.
Step 4 ：The total number of students whose primary motivation is a sense of giving to society is 55.
Step 5 ：The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes.
Step 6 ：Substituting the given values into the formula, we get \( \frac{12}{55} \).
Step 7 ：Final Answer: The probability that the student selected is a junior, given that their primary motivation is a sense of giving to society is \(\boxed{\frac{12}{55}}\) or approximately \(\boxed{0.218}\).
