1. **State the problem:** We want to find the probability of having at most 2 rainy days in 5 days, given each day has a 40% chance of rain. 2. **Identify the distribution:** This is a binomial probability problem where the number of trials $n=5$, probability of success (rain) $p=0.4$, and we want $P(X \leq 2)$ where $X$ is the number of rainy days. 3. **Formula:** The binomial probability mass function is $$P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$$ where $k$ is the number of successes. 4. **Calculate $P(X \leq 2)$:** This is the sum of probabilities for $k=0,1,2$: $$P(X \leq 2) = P(X=0) + P(X=1) + P(X=2)$$ 5. **Calculate each term:** - $P(X=0) = \binom{5}{0} (0.4)^0 (0.6)^5 = 1 \times 1 \times 0.6^5 = 0.07776$ - $P(X=1) = \binom{5}{1} (0.4)^1 (0.6)^4 = 5 \times 0.4 \times 0.6^4 = 5 \times 0.4 \times 0.1296 = 0.2592$ - $P(X=2) = \binom{5}{2} (0.4)^2 (0.6)^3 = 10 \times 0.16 \times 0.216 = 10 \times 0.03456 = 0.3456$ 6. **Sum the probabilities:** $$P(X \leq 2) = 0.07776 + 0.2592 + 0.3456 = 0.68256$$ 7. **Interpretation:** There is approximately a 68.3% chance of having at most 2 rainy days in 5 days.