Problem
A probability experiment is conducted in which the sample space of the experiment is $S=\{1,2,3,4,5,6,7,8,9,10,11,12\}$, event $F=\{3,4,5,6,7\}$, and event $G=\{7,8,9,10\}$. Assume that each outcome is equally likely. List the outcomes in F or G. Find $P(F$ or $G)$ by counting the number of outcomes in $F$ or $G$. Determine $P(F$ or $G)$ using the general addition rule. List the outcomes in F or G. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. F or $G=\{\}$ (Use a comma to separate answers as needed.) B. $\mathrm{F}$ or $\mathrm{G}=\{\}$
Solution
Step 1 ：The question is asking for the outcomes that are in either event F or event G. In set theory, this is known as the union of two sets. The union of two sets is a set that contains all the elements that are in either one of the sets or in both. In this case, we need to find the union of sets F and G.
Step 2 ：Event F is defined as \(F = \{3, 4, 5, 6, 7\}\)
Step 3 ：Event G is defined as \(G = \{7, 8, 9, 10\}\)
Step 4 ：The union of F and G, denoted as F or G, is \(F \cup G = \{3, 4, 5, 6, 7, 8, 9, 10\}\)
Step 5 ：Final Answer: \(\boxed{\{3, 4, 5, 6, 7, 8, 9, 10\}}\)
