Answer the following posterior probability problem:

We know that SARS-CoV2 was circulating, perhaps widely, in southern California as early as the beginning of February 2020. Many cases, particularly in young people, are mild or even asymptomatic. Health clinics now provide antibody tests, which are tests for whether your immune system has previously been exposed to the SARS-CoV-2 virus and recovered. People who have these antibodies may have immunity to future exposure. Which of the following is/are synonymous with posterior probability, also known as the positive predictive value? Select all that apply. Note: Wrong answers result in 50% points deduction on this question. Please choose wisely. a. Conditional probability, P(COVID19 | +) b. Prevalence c. Bayesian probability d. Sensitivity Which of the following is/are synonymous with P(+ | COVID-19)? O a. Prevalence O b. 1 - Specificity O 0' Sensitivity 0 d. Specificity Which of the following is/are synonymous with P(COVID-19)? O a. Prevalence O b. 1 - Specificity O c. Specificity O d. SensitivityDrag and drop the various terms into the correct boxes to compute the posterior probability of you having the COVlD-19. (sensitivity * prevalence) + (1 specificity) * P(COVID |+) = (specificity * prevalence) specificity (1 - prevalence) (sensitivity * prevalence) prevalence (1 - sensitivity) Compute a posterior probability of you having the COVlD-19, i.e., P(COV|D|+), given that you tested + to the antibody test. Assume sensitivity = specificity = 90% and prevalence as you computed in Q29. 0 a. 0.03967 0 b. 0.0625 0 c. 0.00587 0 d. 0.026367 0 e. 0.0397 0 f. 0.0497 Suppose a posterior probability was 0.05 for a COVID test. What would be your conclusion? O a. If you had a positive antibody test for COVID, there is a 5% chance that you actually had COVID O b. Every 5th person has COVID and you are one of them O c. If you had a 5% chance of testing positive, you will have COVIDSuppose there are 115,192 confirmed COVID-19 cases in California with a population of 39.5 million people, what is the prevalence? O a. 3 out of every 100 people O b. 3% O c. 33.333% O d. 3 out of every 1000 people