Final answer:
The probability of exactly two babies out of 1,000 healthy babies being born deaf is approximately 0.2707, or 27.07%.
Step-by-step explanation:
The probability that exactly two babies were born deaf out of a survey of 1,000 healthy babies can be found using the binomial distribution formula. In this case, the probability of a single baby being born deaf is 2/1000 = 0.002. The formula for calculating the probability of exactly two successes in n trials is:
P(X = k) = (n C k) * p^k * (1 - p)^(n - k)
Substituting the values, we have:
P(X = 2) = (1000 C 2) * (0.002)^2 * (1 - 0.002)^(1000 - 2)
Calculating these values using a calculator, we find that the probability is approximately 0.2707, or 27.07%.