A probability experiment is conducted in which the sample space of the experiment is $S=\{4,5,6,7,8,9,10,11,12,13,14,15\}$, event $E=\{4,5,6,7\}$ and event $\mathrm{G}=\{10,11,12,13\}$. Assume that each outcome is equally likely. List the outcomes in $\mathrm{E}$ and $\mathrm{G}$. Are $\mathrm{E}$ and $\mathrm{G}$ mutually exclusive?
List the outcomes in $\mathrm{E}$ and $\mathrm{G}$. Choose the correct answer below.
A. $E$ and $G=\{$ T
(Use a comma to separate answers as needed.)
B. $E$ and $G=\{\}$
Are $E$ and $G$ mutually exclusive?
A. Yes, because the events $E$ and $G$ have no outcomes in common
B. No, because the events $E$ and $G$ have outcomes in common.
C. No, because the events $E$ and $G$ have at least one outcome in common.
D. Yes, because the events $E$ and $G$ have at least one outcome in common
Answer
\(\boxed{\text{Yes, because the events E and G have no outcomes in common.}}\)
Step 1 ：The outcomes in event E are 4, 5, 6, 7.
Step 2 ：The outcomes in event G are 10, 11, 12, 13.
Step 3 ：There are no common outcomes between E and G.
Step 4 ：Therefore, E and G are mutually exclusive.
Step 5 ：\(\boxed{E \text{ and } G = \{4,5,6,7,10,11,12,13\}}\)
Step 6 ：\(\boxed{\text{Yes, because the events E and G have no outcomes in common.}}\)
