probability experiment is conducted in which the sample space of the experiment is $=\{6,7,8,9,10,11,12,13,14,15,16,17\}$, event $F=\{8,9,10,11,12,13\}$, and event $G=\{12,13,14,15\}$. Assume nat each outcome is equally likely. List the outcomes in $F$ or $G$. Find $P(F$ or $G)$ by counting the number of outcomes in or $\mathrm{G}$. Determine $\mathrm{P}(\mathrm{F}$ or $\mathrm{G})$ using the general addition rule. ist the outcomes in F or G. Select the correct choice below and, if necessary, fill in the answer box to complete your hoice. A. $F$ or $G=\{8,9,10,11,12,13,14,15\}$ (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 $G$. $P(F$ or $G)=$ (Type an integer or a decimal rounded to three decimal places as needed.) Determine $\mathrm{P}(\mathrm{F}$ or $\mathrm{G})$ 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 olaces as needed.) A. $\mathrm{P}(\mathrm{F}$ or $\mathrm{G})=\square+\square-\square=$ B. $P(F$ or $G)=\square+\square=\square$ (1) Time Remaining: 00:09:21 Next
Solution
Step 1 ：The outcomes in F or G are found by taking the union of the two sets F and G. The union of two sets is the set of elements that are in either set, or in both. So, the outcomes in F or G are \(\{8,9,10,11,12,13,14,15\}\).
Step 2 ：The probability of F or G is found by counting the number of outcomes in F or G and dividing by the total number of outcomes in the sample space. So, the probability of F or G is \(\frac{8}{12} = 0.667\).
Step 3 ：The probability of F or G using the general addition rule is found by adding the probabilities of F and G and subtracting the probability of both F and G. So, the probability of F or G using the general addition rule is also \(0.667\).
Step 4 ：Final Answer: The outcomes in F or G are \(\boxed{\{8,9,10,11,12,13,14,15\}}\). The probability of F or G by counting the number of outcomes in F or G is \(\boxed{0.667}\). The probability of F or G using the general addition rule is also \(\boxed{0.667}\).
