The probability that four randomly selected adults have health insurance, given that 66% of adults are insured, is calculated using the formula (0.66)^4. This results in a probability of approximately 0.1877, or 18.77%. The assumption is based on a very large population size, which allows for the use of the binomial probability model. The calculation reflects the likelihood of all four individuals being insured under the given percentage. Understanding this probability can help in assessing health insurance coverage among small groups.