QUESTION 25 - 1 POINT Fill in the following contingency table on your own paper and find the number of students who both go to the beach AND go to the mountains. \begin{tabular}{|c|c|c|c|} \hline Students & go to the mountains & do not go to the mountains & Total \\ \hline go to the beach & & & 36 \\ \hline do not go to the beach & & 21 & \\ \hline Total & 48 & & 95 \\ \hline \end{tabular} Provide your answer below: FEEDBACK
Solution
Step 1 ：Given values are: Total number of students, \(P_{Total} = 95\), number of students who go to the beach, \(P_B = 36\), number of students who go to the mountains, \(P_M = 48\), and number of students who do not go to the beach, \(P_N = 21\).
Step 2 ：Calculate the number of students who either go to the beach or go to the mountains, \(P_{B \cup M} = P_{Total} - P_N\). Substituting the given values, we get \(P_{B \cup M} = 95 - 21 = 74\).
Step 3 ：Calculate the number of students who both go to the beach and go to the mountains, \(P_{B \cap M} = P_B + P_M - P_{B \cup M}\). Substituting the given values, we get \(P_{B \cap M} = 36 + 48 - 74 = 10\).
Step 4 ：Final Answer: The number of students who both go to the beach AND go to the mountains is \(\boxed{10}\).
