Problem
A probability experiment is conducted in which the sample space of the experiment is $S=\{9,10,11,12,13,14,15,16,17,18,19,20\}$. Let event $E=\{12,13,14,15,16,17,18,19,20\}$. Assume each outcome is equally likely. List the outcomes in $E^{C}$. Find $P\left(E^{C}\right)$. List the outcomes in $E^{C}$. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $E^{C}=\{\}$ (Use a comma to separate answers as needed.) B. $E^{C}=\{\}$ Clear all
Solution
Step 1 ：The sample space of the experiment is $S=\{9,10,11,12,13,14,15,16,17,18,19,20\}$ and event $E=\{12,13,14,15,16,17,18,19,20\}$.
Step 2 ：The complement of an event E, denoted by $E^{C}$, is the set of all outcomes in the sample space that are not in E.
Step 3 ：So, we need to find all the outcomes in the sample space S that are not in E.
Step 4 ：The outcomes in $E^{C}$ are $\{9, 10, 11\}$
Step 5 ：Final Answer: $E^{C}=\boxed{\{9,10,11\}}$
