The article, Remdesivir in adults with severe COVID-19: a randomised, double-blind, placebo-controlled, multicentre trial, Lancet, 395(10236), pp. 1569–1578, May 16, 2020, by Y. Wang and et. al., reports the following study for the treatment of severe cases of SARS-CoV-2 virus infection with an experimental medicine, Remdesivir, originally made for Ebola. “237 patients were enrolled and randomly assigned to a treatment group or a control group (158 to Remdesivir and 79 to placebo).” At the conclusion of the study, which took 28 days, 22 people from the Remdesivir group and 10 people from the placebo group passed away. Suppose that one patient was selected.
(a) If the selected patient is from the treatment group (Remdesivir-group), what is the probability that the patient survived to the conclusion of the study?
(b) If the selected patient is from the control group (Placebo-group), what is the probability that the patient died before the conclusion of the study?
(c) If the selected patient survived to the conclusion of the study, what is the probability that the patient received the medicine?
(d) If the selected patient died before the conclusion of the study, what is the probability that the patient received the placebo?