Pfizer would like to study the side effects (i.e., fever and muscle ache) of their COVID-19 vaccination. Its research team collect data and show that 73% of vaccinated patients had a side effect, and 37% of patients who received a placebo had a side effect. The team also knows that 45% of sampled patients were vaccinated and the rest had a placebo. As such, the team would like to determine the following; (1) the probability that a patient received a placebo, (2) among vaccinated patients, t