Final answer:
Calculating the probability using the complement rule reveals that it is almost certain (nearly 100%) that at least one out of 10 randomly sampled American adults will have had chickenpox, given a 90% historical infection rate.
Step-by-step explanation:
The probability that at least 1 out of 10 randomly sampled American adults has had chickenpox, given a 90% rate of infection by adulthood, can be found using the complement rule. The complement rule states that the probability of at least one event occurring is equal to 1 minus the probability of none of the events occurring. Therefore, we first calculate the probability that none of the 10 adults have had chickenpox, which is (0.10)^10, because there is a 10% chance for each individual not to have had chickenpox. Since we need the probability of at least 1 having had chickenpox, we subtract this from 1.
The calculation is: 1 - (0.10)^10 = 1 - (a very small number close to 0), which is approximately 1. Thus, it is almost certain that at least one adult in a random sample of 10 has had chickenpox, reinforcing the high prevalence of the disease in the United States as indicated by the National Vaccine Information Center.