Problem
15 students were asked to choose between the broad categories of Arts, Science, and Math as their preferred area of study. \begin{tabular}{|c|c|c|} \hline Respondent & Gender & Preference \\ \hline 1 & Female & Arts \\ \hline 2 & Male & Science \\ \hline 3 & Male & Math \\ \hline 4 & Female & Arts \\ \hline 5 & Female & Math \\ \hline 6 & Male & Science \\ \hline 7 & Male & Math \\ \hline 8 & Male & Math \\ \hline 9 & Female & Arts \\ \hline 10 & Male & Arts \\ \hline 11 & Male & Science \\ \hline 12 & Female & Science \\ \hline 13 & Female & Math \\ \hline 14 & Male & Arts \\ \hline 15 & Female & Arts \\ \hline \end{tabular} What is the probability that a respondent is male and prefers Arts? $6 / 15$ $2 / 15$ $10 / 15$ $8 / 15$
Solution
Step 1 ：Given data of 15 students with their gender and preference of study.
Step 2 ：From the data, we can see that there are 2 male students who prefer Arts.
Step 3 ：The total number of students is 15.
Step 4 ：To find the probability that a respondent is male and prefers Arts, we divide the number of male students who prefer Arts by the total number of students.
Step 5 ：Calculating the probability gives us \(\frac{2}{15}\).
Step 6 ：Final Answer: The probability that a respondent is male and prefers Arts is \(\boxed{\frac{2}{15}}\).
