Part 2 of 3 Polnta; 0 of 1 A probability experiment is conducted in which the sample space of the experiment is \( S=\{9,10,11,12,13,14,15,16,17,18,19,20\} \), event \( F=\{11,12,13,14,15\} \), and event \( G=\{15,16,17,18\} \) 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 \( G=\{11,12,13,14,15,16,17,18\} \) (Use a comma to separate answers as needed.) B. \( F \) or \( G=\{ \} \) Find \( P(F \) or \( G) \) by counting the number of outcomes in \( F \) or \( G \). \[ P(F \text { or } G)=\square \] (Type an integer or a decimal rounded to three decimal places as needed.)

**Step 1. List the outcomes in \( F \) or \( G \).** The event \( F \) is given by \[ F = \{11, 12, 13, 14, 15\} \] and the event \( G \) is \[ G = \{15, 16, 17, 18\}. \] The union of \( F \) and \( G \) (i.e., \( F \) or \( G \)) is \[ F \cup G = \{11, 12, 13, 14, 15, 16, 17, 18\}. \] Thus, the correct choice is: A. \( F \text{ or } G = \{11,12,13,14,15,16,17,18\} \). --- **Step 2. Find \( P(F \text{ or } G) \) by counting the number of outcomes in \( F \) or \( G \).** 1. Count the outcomes in \( F \cup G \): \[ \{11,12,13,14,15,16,17,18\} \text{ contains } 8 \text{ outcomes.} \] 2. Count the total number of outcomes in the sample space \( S \): \[ S = \{9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\} \quad \Rightarrow \quad |S| = 12. \] 3. Thus, the probability is \[ P(F \text{ or } G) = \frac{\text{Number of outcomes in } F \cup G}{\text{Number of outcomes in } S} = \frac{8}{12} = \frac{2}{3} \approx 0.667. \] --- **Step 3. Determine \( P(F \text{ or } G) \) using the general addition rule.** The general addition rule for probabilities is \[ P(F \cup G) = P(F) + P(G) - P(F \cap G). \] 1. Calculate \( P(F) \): \[ |F| = 5 \quad \Rightarrow \quad P(F) = \frac{5}{12}. \] 2. Calculate \( P(G) \): \[ |G| = 4 \quad \Rightarrow \quad P(G) = \frac{4}{12}. \] 3. Determine the intersection \( F \cap G \): \[ F \cap G = \{15\} \quad \Rightarrow \quad |F \cap G| = 1, \quad P(F \cap G) = \frac{1}{12}. \] 4. Applying the rule: \[ P(F \cup G) = \frac{5}{12} + \frac{4}{12} - \frac{1}{12} = \frac{8}{12} = \frac{2}{3} \approx 0.667. \] --- **Final Answers:** - The outcomes in \( F \) or \( G \) are: \( \{11,12,13,14,15,16,17,18\} \). - \( P(F \text{ or } G) = \frac{2}{3} \) (or approximately 0.667).