A probability experiment is conducted in which the sample space of the experiment is $\mathrm{S}=\{1,2,3,4,5,6,7,8,9,10,11,12\}$. Let event $E=\{2,3,4,5,6,7\}$ and event $F=\{6,7,8,9\}$. List the outcomes in $E$ and $\mathrm{F}$. 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. \{\}
Answer
\(\boxed{\text{The outcomes in E are } \{2,3,4,5,6,7\} \text{ and the outcomes in F are } \{6,7,8,9\}. \text{ The events E and F are not mutually exclusive.}}\)
Step 1 ：The outcomes in event E are \{2,3,4,5,6,7\}.
Step 2 ：The outcomes in event F are \{6,7,8,9\}.
Step 3 ：Two events are mutually exclusive if they cannot both occur at the same time, that is, the intersection of the events is empty.
Step 4 ：In this case, the events E and F both include the outcomes 6 and 7, so they are not mutually exclusive.
Step 5 ：\(\boxed{\text{The outcomes in E are } \{2,3,4,5,6,7\} \text{ and the outcomes in F are } \{6,7,8,9\}. \text{ The events E and F are not mutually exclusive.}}\)
