Problem
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 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 $G=\{3,4,5,6,7,8,9,10\}$ (Use a comma to separate answers as needed.) B. $F$ or $G=\{\}$ Find $\mathrm{P}(\mathrm{F}$ or $\mathrm{G})$ by counting the number of outcomes in $\mathrm{F}$ or $\mathrm{G}$. \[ P(F \text { or } G)= \] (Type an integer or a decimal rounded to three decimal places as needed.)
Solution
Step 1 ：The outcomes in F or G are \(\{3,4,5,6,7,8,9,10\}\).
Step 2 ：The probability of F or G is calculated by dividing the number of outcomes in F or G by the total number of outcomes in the sample space. This gives us \(\frac{8}{12} = 0.6666666666666666\).
Step 3 ：Rounding to three decimal places, the probability of F or G is \(\boxed{0.667}\).
