Final answer:
To calculate the probability that all 20 people selected at random are 65 or older, we use the binomial probability formula with a success probability of 0.118 for each trial and 20 trials. The computation would result in a very small decimal value.
Step-by-step explanation:
The question pertains to the subject of probability and requires the application of the binomial probability formula. The formula for the probability of having exactly k successes in n independent Bernoulli trials is given by P(X=k) = C(n, k) * pk * (1-p)n-k where C(n, k) is the binomial coefficient, p is the probability of success on a single trial, and (1-p) is the probability of failure.
To find the probability that all 20 people selected at random are 65 or older, we use p = 0.118 (since 11.8% of the population is 65 or older) and n = 20. Thus, k would be 20 because we are looking for the probability that all 20 people are 65 or older. The calculation would then be based on the binomial probability formula. Since the computation might be complex and the probability extremely low, it is expected that the answer will be a very small decimal number, which should be rounded to the nearest thousandth as requested.