1. **State the problem:** We want to find the probability that it will rain on at most one day during the 7 days the Hiking Club is camping, given the probability of rain on any day is 0.71. 2. **Identify the distribution:** This is a binomial probability problem where the number of trials $n=7$, the probability of success (rain) on each trial $p=0.71$, and we want $P(X \leq 1)$ where $X$ is the number of rainy days. 3. **Formula:** The binomial probability formula is $$P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$$ where $\binom{n}{k}$ is the binomial coefficient. 4. **Calculate $P(X=0)$:** $$P(X=0) = \binom{7}{0} (0.71)^0 (0.29)^7 = 1 \times 1 \times 0.29^7 = 0.29^7$$ Calculate $0.29^7$: $$0.29^7 \approx 0.000615$$ 5. **Calculate $P(X=1)$:** $$P(X=1) = \binom{7}{1} (0.71)^1 (0.29)^6 = 7 \times 0.71 \times 0.29^6$$ Calculate $0.29^6$: $$0.29^6 \approx 0.00212$$ Then: $$P(X=1) = 7 \times 0.71 \times 0.00212 \approx 7 \times 0.001505 = 0.010535$$ 6. **Sum probabilities:** $$P(X \leq 1) = P(X=0) + P(X=1) = 0.000615 + 0.010535 = 0.01115$$ 7. **Round to nearest thousandth:** $$0.01115 \approx 0.011$$ **Final answer:** The probability that it will rain on at most one of the seven days is approximately **0.011**.