Hello, may I please get help regarding this section? I very much appreciate the help, thank you!

Context: 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.

Problem 1: Which of the following is/are synonymous with posterior probability, also known as the positive predictive value? Select all that apply.

a. Sensitivity

b. Conditional probability, P(COVID-19 | +)

c. Bayesian probability

d. Prevalence

Problem 2: Which of the following is synonymous with P(+ | COVID-19)?

a. Sensitivity

b. Specificity

c. 1 - Specificity

d. Prevalence

Problem 3: Which of the following is synonymous with P(COVID-19)?

a. Sensitivity

b. Prevalence

c. Specificity

d. 1 - Specificity

Problem 4: Suppose there are 115,192 confirmed COVID-19 cases in California with a population of 39.5 million people, what is the prevalence?

a. 3%

b. 3 out of every 100 people

c. 3 out of every 1000 people

d. 33.333%

Problem 5: Compute a posterior probability of you having the COVID-19, i.e., P(COVID|+), given that you tested + to the antibody test. Assume sensitivity = specificity = 90% and prevalence as you computed in Q29.

a. 0.0497

b. 0.03967

c. 0.00587

d. 0.0625

e. 0.0397

f. 0.026367

Part 6: Suppose a posterior probability was 0.05 for a COVID test. What would be your conclusion?

a. Every 5th person has COVID and you are one of them

b. If you had a 5% chance of testing positive, you will have COVID

c. If you had a positive antibody test for COVID, there is a 5% chance that you actually had COVID