Final Answer:
(a) The events of births and deaths are assumed to be independent due to their rarity.
(b) For a community of 1,000 people: P(9 births) ≈ 0.1826, P(9 deaths) ≈ 0.0590, P(15 births) ≈ 0.0000, P(15 deaths) ≈ 0.0000.
(c) For a community of 1,500 people: P(9 births) ≈ 0.2739, P(9 deaths) ≈ 0.0884, P(15 births) ≈ 0.0001, P(15 deaths) ≈ 0.0001.
(d) For a community of 750 people: P(9 births) ≈ 0.0913, P(9 deaths) ≈ 0.0295, P(15 births) ≈ 0.0000, P(15 deaths) ≈ 0.0000.
Step-by-step explanation:
(a) The assumption of independence is made due to the rarity of births and deaths.
(b), (c), (d) The probabilities are calculated using the binomial probability formula, where P(X = k) = C(n, k) * p^k * (1 - p)^(n - k), where n is the number of trials, k is the number of successes, p is the probability of success, and C(n, k) is the binomial coefficient. The values are rounded to four decimal places.