1. **Problem Statement:** Suppose 40% of a large population of registered voters favor the candidate Nimal. A random sample of 5 voters is selected. We want to find the probability that none of the 5 voters favor Nimal. 2. **Identify the distribution:** This is a binomial probability problem where: - Number of trials $n = 5$ - Probability of success (favoring Nimal) $p = 0.4$ - Probability of failure $q = 1 - p = 0.6$ - Number of successes $k = 0$ 3. **Formula:** The binomial probability formula is: $$P(X = k) = \binom{n}{k} p^k q^{n-k}$$ where $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ is the binomial coefficient. 4. **Calculate the probability:** For $k=0$, $$P(X=0) = \binom{5}{0} (0.4)^0 (0.6)^5 = 1 \times 1 \times (0.6)^5 = (0.6)^5$$ 5. **Evaluate:** $$ (0.6)^5 = 0.6 \times 0.6 \times 0.6 \times 0.6 \times 0.6 = 0.07776 $$ 6. **Interpretation:** The probability that none of the 5 voters favor Nimal is approximately 0.07776 or 7.776%.