1. Suppose that 8% of a population is infected with a virus. There are no obvious symptoms that can be used to recognize carriers, thus individuals must be selected at random and tested. We can assume the test to detect infected individuals is 100% accurate. a. If a sample of 10 individuals from the population are tested, what is the probability that at most one of them is infected? (2px) b. One researcher's goal is to nd at least one person who is infected with the virus for observation. If she samples too few people, there is a risk of not nding any carriers, while testing too many people will waste valuable testing resources. What is the minimum sample size she needs in order to detect at least one infected individual with a probability of at least 90%? Justify your answer. (2p!)