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 $\mathrm{F}=\{3,4,5,6,7\}$, and event $\mathrm{G}=\{7,8,9,10\}$. Assume that each outcome is equally likely. List the outcomes in $\mathrm{F}$ or $\mathrm{G}$. 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. (Use a comma to separate answers as needed.) B. $\mathrm{F}$ or $\mathrm{G}=\{\}$ Find $\mathrm{P}(\mathrm{F}$ or $\mathrm{G})$ by counting the number of outcomes in $\mathrm{F}$ or $\mathrm{G}$. \[ P(F \text { or } G)=0.667 \] (Type an integer or a decimal rounded to three decimal places as needed.) Determine $P(F$ or $G)$ using the-general addition rule. 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. $P(F$ or $G)=\square+\square=$ B. $P(F$ or $G)=\square+\square-\square=$

Step 1 ：The outcomes in F or G are the union of the sets F and G. So, F or G = \(\{3, 4, 5, 6, 7, 8, 9, 10\}\).

Step 2 ：The probability of F or G by counting the outcomes is the number of outcomes in F or G divided by the total number of outcomes in the sample space. So, \(P(F \text{ or } G) = \frac{8}{12} = 0.667\).

Step 3 ：The general addition rule for probability states that the probability of F or G is equal to the probability of F plus the probability of G minus the probability of both F and G. So, \(P(F \text{ or } G) = P(F) + P(G) - P(F \text{ and } G)\).

Step 4 ：The probability of an event is the number of outcomes in the event divided by the total number of outcomes in the sample space. So, \(P(F) = \frac{5}{12} = 0.417\) and \(P(G) = \frac{4}{12} = 0.333\).

Step 5 ：The probability of both F and G is the probability of the intersection of F and G, which is the number of outcomes in both F and G divided by the total number of outcomes in the sample space. So, \(P(F \text{ and } G) = \frac{1}{12} = 0.083\).

Step 6 ：Substituting these values into the general addition rule gives \(P(F \text{ or } G) = 0.417 + 0.333 - 0.083 = 0.667\).

Step 7 ：Final Answer: The outcomes in F or G are \(\boxed{\{3, 4, 5, 6, 7, 8, 9, 10\}}\). The probability of F or G by counting the outcomes is \(\boxed{0.667}\). The probability of F or G using the general addition rule is also \(\boxed{0.667}\).