A company with 10 employees decides to test them for COVID-19 before they go back to work in person. From available data, they determine that the probability of each employee being ill is 0.01. The employees have not been in contact with each other for a while, so the events Employee i is ill, for 1 i 10, are modeled as independent. If an employee is ill, the test is positive with probability 0.98. If they are not ill, the test is positive with probability 0.05.

The company tests all employees. What is the probability that there is at least one positive test? If there is at least one positive test, what is the probability that nobody is ill? If you make any independence or conditional independence assumptions, please justify them.