Please Help...

Given the numerous discussions around vaccines and clinical trials that we have had this year, we would like you to get a deeper understanding of what some of these terms mean. We will look at a simplified version of vaccine trial information and try to understand what vaccine efficacy really means. There is much more that can be extrapolated from vaccine trial data, but we will be limiting ourselves to a small subset. Table 1 is a simplified version of Table 3 from the paper that discusses the efficacy of BNT162b2, the Pfizer-made vaccine for COVID-19 Efficacy Endpoint Number of COVID Cases Number of COVID Cases Vaccine Efficacy, % Subgroup in Vaccine Group (N=17,397) in Placebo Group (N=17,498) Overall 8 162 95.0 Age Group 16-55 years 5 (N=9897) 114 (N=9955) 95.6 >55 years 3 (N=7500) 48 (N=7543) 93.7 >65 years 1 (N=3848) 19 (N=3880) 94.7 >75 years O (N=774) 5 (N=785) 100.0 Table 1: Trial data for the Pfizer made vaccine for COVID-19. Source: Link 1.1. Starting with the basics Answer the questions using table 1. Let the event V denote that a random participant was in the vaccine group, and the event S denote that the participant got sick. (a) What's the probability that a random participant gets sick, regardless of what group they were in? What about for each participant group (vaccine and placebo)? Clearly state the symbols you use for each event and the conditional and unconditional probability. (b) Given that a participant got sick, what is the probability that they were in the vaccine group? This should be a direct Bayes' Rule calculation. (c) Is this enough data to convince you to get the vaccine? Is there anything important that this table is missing