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.)

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UpStudy AI · Accepted Answer

**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).
**Outcomes in $$ F $$ or $$ G $$:** 11, 12, 13, 14, 15, 16, 17, 18 **Probability $$ P(F $$ or $$ G) $$:** 0.667

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