Show your calculations and logic - and USE EXCEL FORMULAS to solve the following problems where applicable.

The Centers for Disease Control (CDC) estimates that the current prevalence of COVID infection in the population in a particular state in US is 1% (i.e., 1% of the population currently is estimated to have the COVID infection). The FDA has recently approved a rapid COVID test which has a reliability as follows,

• If the person tested has COVID infection, the test comes back positive 98% of the times.
• If the person tested does not have COVID infection, the test comes back negative 99% of the times.

Based on this information answer the following questions.

[HINT:It may be helpful to construct a contingency table for this problem.]

(a) A person is selected at random from the state and administered this test and it comes back positive. What is the probability that the person has COVID infection? Please provide your answer in four decimal points and briefly show your working.

(b) 10,000 such tests are administered across the state in a day. How many tests are likely to come back positive? Please briefly show your working.

(c) What is the probability of a person testing negative for COVID and yet having the COVID infection? Please provide your answer in four decimal points and briefly show your working.