A probability experiment is conducted in which the sample space of the experiment is $$ \mathrm{S}=\{9,10,11,12,13,14,15,16,17,18,19,20\} $$, event $$ \mathrm{F}=\{11,12,13,14,15\} $$, and $$ \operatorname{svent} \mathrm{G}=\{15,16,17,16\} $$ 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 ruie. 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. For $$ \mathrm{G}=\{ \} $$ Find $$ P(F $$ or $$ G) $$ by counting the number of outcomes in $$ F $$ or $$ G $$. $$ P(F \text { or } G)=0.667 $$ (Type an integer or a decimal rounded to three decimal places as needed.) Determine P(F or G) using the general addition rute. Select the correct choice below and fill in any answer boxes within your choice. (Type the terms of your expression in the same order as they appear in the original expression. Round to three decimal places as needed.) A. $$ \mathrm{P}(\mathrm{F} $$ or G$$ )= $$ $$ \square $$ $$ + $$ - $$ \square $$ $$ - $$ $$ \square $$ B. $$ P(F $$ or $$ G)=\square+\square=\square $$

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UpStudy AI · Accepted Answer

1. **List the outcomes in $$ F $$ or $$ G $$:**  
 Assume that the intended event is  
  $$ F=\{11,12,13,14,15\} $$ and $$ G=\{15,16,17,18\} $$  
 Then the union of the events (i.e. outcomes that are in $$ F $$ or $$ G $$) is  
  $$
F\cup G=\{11,12,13,14,15,16,17,18\}.
$$

2. **Find $$ P(F $$ or $$ G) $$ by counting outcomes:**  
 The sample space is  
  $$
S=\{9,10,11,12,13,14,15,16,17,18,19,20\}
$$  
 which has 12 outcomes. The union $$ F\cup G $$ has 8 outcomes. Since all outcomes are equally likely,  
  $$
P(F\cup G)=\frac{8}{12}\approx0.667.
$$

3. **Determine $$ P(F $$ or $$ G) $$ using the general addition rule:**  
 The general addition rule states that  
  $$
P(F\cup G)=P(F)+P(G)-P(F\cap G).
$$  
 Calculate each term:  
  - $$ P(F)=\dfrac{5}{12} $$ because $$ F $$ has 5 outcomes.  
  - $$ P(G)=\dfrac{4}{12} $$ because $$ G $$ has 4 outcomes.  
  - The intersection $$ F\cap G $$ is the set of outcomes common to both $$ F $$ and $$ G $$. Since $$ F\cap G=\{15\} $$, we have  
   $$ P(F\cap G)=\dfrac{1}{12} $$.

Substitute these into the formula:  
  $$
P(F\cup G)=\frac{5}{12}+\frac{4}{12}-\frac{1}{12}=\frac{8}{12}\approx0.667.
$$

4. **Select the correct choice for each part:**

- For listing outcomes, the correct answer is:  
  **$$ F $$ or $$ G=\{11,12,13,14,15,16,17,18\} $$.**

- For the probability using counting,  
  $$
P(F\text{ or }G)=0.667.
$$

- For the probability using the general addition rule, the expression is:  
  $$
P(F\text{ or }G)=\frac{5}{12}+\frac{4}{12}-\frac{1}{12}\approx0.667.
$$
**Outcomes in $$ F $$ or $$ G $$:** 11, 12, 13, 14, 15, 16, 17, 18 **Probability $$ P(F $$ or $$ G) $$:** 0.667 **Using the General Addition Rule:** $$ P(F $$ or $$ G) = \frac{5}{12} + \frac{4}{12} - \frac{1}{12} = 0.667 $$

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