Answer Happy

After almost two years of the pandemic, Martina and Robin organise a large party. Each of them invites 50 friends. Martina and Robin want to avoid a super-spreader event, so they send antigen tests along with the invitations. The test they got has a 5% false-positive rate and a 2% false- negative rate. Their idea is straightforward: • If the number of positive tests is higher than what they can expect by chance if no one has covid, they will ask everyone to take a PCR test and only those with a negative PCR will get to come to the party. • If the number of positive tests is below what they would by chance if no one has covid they will not require PCR tests and everyone can come to the party a. If none of the invitees has Covid, how many positive tests should they expect? (Round your answer to the largest integer) At this stage of the pandemic, 1.5% of the population has Covid-19 in any given two weeks. b. What is the probability that someone that tested positive in the antigen test has Covid? (Round your answer to 2 decimal places) c. How would you justify your answer? OA OB OC OD OE PABIYB) PHAB)PB) A. Let A denote being sick and B denote testing positive. Then Pr(B|A) - MADAM AP where Pr(A/B) = 1 -0.02 is the rate of correct positives, Pr(AB9) = 0.05 is the rate of false positives, Pr(B) = 0.015 is the probability of having Covid and Pr(B) = 1 -0.015 is the probability of not having Covid. B. Let A denote being sick and B denote testing positive. Then Pr(BLA) PHABAT where Pr(AB) = 0.02 is the rate of correct positives, Pr(A/B) = 0.05 is the rate of faise positives, Pr(B) = 0.015 is the probability of having Covid and Pr(B) = 1 -0.015 is the probability of not having Covid. C. Let B denote being sick and A denote testing positive. Then Pr(BA) PMDP) PMALPH where Pr(AB) = 1 -0.02 is the rate of correct positives, Pr(A|B“) = 0.05 is the rate of false positives. Pr(B) = 0.015 is the probability of having Covid and Pr(B) = 1-0.015 is the probability of not having Covid. D. Let B denote being sick and A denote testing positive. Then Pr(BA) - NADINE) PAB)/HIMALBATEA where Pr(AB) = 0.02 the rate of correct positives, Pr(A/B) = 0.05 is the rate of false positives, Pr(B) = 0.015 is the probability of having Covid and Pr(B) - 1 -0.015 is the probability of not having Covid. E. None of the above. (Please justify your answer in the comment box) IYABIT)

After they send the invitations, 17 friends have a positive antigen test. Assume none of the invites has met each other in the past month d. Out of the 17 positive antigen tests, what is the probability that at least one of them has Covid? (Round your answer to 2 decimal places) e. How would you justify your answer? OA OB OC OD OB A. Let X-B(n,p) denote a random variable that describes the number of sick individuals out of n = 17 positive antigen tests. p is the probability of being sick conditional on testing positive as per my previous answer. The probability that at least one of them is sick is equivalent to asking Pr(X < 1). Using the Bernoulli distribution formula Pr(x1) - sop' (1-p)" B. Let X-B( np) denote a random variable that describes the number of sick individuals out of n = 17 positive antigen tests. p is the probability of being sick conditional on testing positive as per my previous answer. The probability that at least one of them is sick is equivalent to asking Pr(x > 1) = 1 - Pr(x < 0) Using the Bernoulli distribution formula Pr(x < 0) - M P (1 - p)". C. Let X-B(n,p) denote a random variable that describes the number of sick individuals out of n = 17 positive antigen tests. p is the probability of being sick conditional on testing positive as per my previous answer. The probability that at least one of them is sick is equivalent to asking Pr(x < 1). Using the Bernoulli distribution formula Pr(x > 1) - 10 p! (1 - ) D. Let X-B(1, p) denote a random variable that describes the number of sick individuals out of n = 17 positive antigen tests. p is the probability of being sick conditional on testing positive as per my previous answer. The probability that at least one of them is sick is equivalent to asking Pr(X < 0). Using the Bernoulli distribution formula Pr(x 20) = ° (1 - 1) E. None of the above (Please justify your answer in the comment box)