1. **Stating the problem:** We are given the probability of seeing one penguin in an hour as $\frac{6}{24} = 0.25$ and the probability of seeing more than one penguin in an hour is 0. We want to find the probability of seeing exactly 5 penguins in 24 hours, treating this as a binomial experiment. 2. **Formula used:** For a binomial experiment, the probability of exactly $k$ successes in $n$ trials is given by: $$P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$$ where $n$ is the number of trials, $k$ is the number of successes, and $p$ is the probability of success in one trial. 3. **Identify parameters:** Here, $n = 24$ (hours), $k = 5$ (penguins), and $p = 0.25$ (probability of seeing one penguin in an hour). 4. **Calculate the binomial coefficient:** $$\binom{24}{5} = \frac{24!}{5! \times (24-5)!} = 42504$$ 5. **Calculate the probability:** $$P(X=5) = 42504 \times (0.25)^5 \times (0.75)^{19}$$ 6. **Calculate powers:** $$(0.25)^5 = 0.0009765625$$ $$(0.75)^{19} \approx 0.013363$$ 7. **Multiply all parts:** $$P(X=5) = 42504 \times 0.0009765625 \times 0.013363 \approx 0.555$$ **Final answer:** The probability of seeing exactly 5 penguins in 24 hours is approximately **0.555** (rounded to three decimal places).