Problem
A probability experiment is conducted in which the sample space of the experiment is $S=\{4,5,6,7,8,9,10,11,12,13,14,15\}$. Let event $E=\{5,6,7,8,9,10\}$ and event $F=\{9,10,11,12\}$. List the outcomes in $E$ and F. Are $\mathrm{E}$ and $\mathrm{F}$ mutually exclusive? List the outcomes in E and F. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (Use a comma to separate answers as needed.) B. \{\}
Solution
Step 1 ：Define the events E and F as E = {5, 6, 7, 8, 9, 10} and F = {9, 10, 11, 12}.
Step 2 ：Find the intersection of E and F, which is {9, 10}.
Step 3 ：Since the intersection of E and F is not empty, E and F are not mutually exclusive.
Step 4 ：\(\boxed{\text{The outcomes in E are } \{5,6,7,8,9,10\} \text{ and the outcomes in F are } \{9,10,11,12\}. \text{ E and F are not mutually exclusive.}}\)
