About $15 \%$ of the population of a large country is nervous around strangers. If two people are randomly selected, what is the probability both are nervous around strangers? What is the probability at least one is nervous around strangers? Assume the events are independent. (b) The probability that at least one person is nervous around strangers is (Round to four decimal places as needed.)

Step 1 ：The problem states that about 15% of the population of a large country is nervous around strangers. If two people are randomly selected, we are asked to find the probability that both are nervous around strangers and the probability that at least one is nervous around strangers. We are to assume the events are independent.

Step 2 ：First, we find the probability that both people are nervous around strangers. Since the events are independent, we can simply multiply the probabilities together. The probability that one person is nervous around strangers is 15% or 0.15. So, the probability that both are nervous is \(0.15 * 0.15\).

Step 3 ：Next, we find the probability that at least one person is nervous around strangers. This is equivalent to 1 minus the probability that neither person is nervous. The probability that one person is not nervous is 85% or 0.85. So, the probability that neither person is nervous is \(0.85 * 0.85\). Therefore, the probability that at least one person is nervous is \(1 - (0.85 * 0.85)\).

Step 4 ：Calculating these probabilities gives us the final answers. The probability that both people are nervous around strangers is \(\boxed{0.0225}\) and the probability that at least one person is nervous around strangers is \(\boxed{0.2775}\).