1. The problem asks to list the elements of sample space $S$ corresponding to event $E$ where at least two of the rivers are safe for fishing. 2. Each element in $S$ is a three-letter code representing the safety of three rivers: $F$ for not safe (Fail) and $N$ for safe (No problem). 3. "At least two rivers are safe" means the element must have at least two $N$s. 4. Check each option: - a. $\{FFF, FFN, FNF, NNN\}$: Only $NNN$ has three $N$s, others have fewer than two $N$s. - b. $\{FFF, FFN, FNF, NFN\}$: $NFN$ has two $N$s, but $FFN$ and $FNF$ have only one $N$, $FFF$ has none. - c. $\{FFF, FFF, FNF, NFF\}$: $NFF$ has one $N$, others have none. - d. $\{FFF, FFN, FNF, NFF\}$: $FFN$, $FNF$, and $NFF$ each have one $N$, $FFF$ has none. 5. None of the options except option a has $NNN$ which has three $N$s, but option a also includes $FFF$, $FFN$, and $FNF$ which do not have at least two $N$s. 6. The correct set for "at least two rivers safe" should include elements with two or three $N$s. 7. The only option that includes $NNN$ (three $N$s) is option a, but it also includes elements with fewer than two $N$s. 8. None of the options perfectly match the event "at least two rivers safe". 9. However, option a includes $NNN$ which is the only element with at least two $N$s, so it is the closest correct option. Final answer: Option a