Vaccine A and B are given to 20% and 50% of the individuals in Country X, respectively, to protect them from becoming infected with Covid-19. The remaining persons have not received any vaccinations against Covid-19. None of them received more than one vaccination. The rates of Covid-19 infection for people vaccinated with Vaccine A, people vaccinated with Vaccine B, and unprotected people are known to be 20%, 10%, and 50%, respectively. What is the likelihood of a person being unvaccinated if they are randomly chosen and discovered to be infected with Covid-19?

Vaccine A and B are given to 20% and 50% of the individuals in Country X, respectively, to protect them from becoming infected with Covid-19. The remaining persons have not received any vaccinations against Covid-19. None of them received more than one vaccination. The rates of Covid-19 infection for people vaccinated with Vaccine A, people vaccinated with Vaccine B, and unprotected people are known to be 20%, 10%, and 50%, respectively. What is the likelihood of a person being unvaccinated if they are randomly chosen and discovered to be infected with Covid-19?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

2. A group of doctors at a specific hospital believes that the normal survival rate for patients with extensive burns will significantly increase with the use of new fluid plasma compresses. Before the new treatment, the survival rate for extensive burn patients at the hospital was about 40%. Using the new compresses, the hospital found that 48 out of 90 patients with extensive burns survived. Does this provide sufficient evidence for the hospital to try to market the new fluid plasma compresses to other hospitals? Answer this question using a = 0.05.
A study was performed to test the effectiveness of a new treatment for migraines. There were 125 patients in the study. Of these, 60 were randomly assigned to receive the standard treatment and 65 to receive the new treatment. All were instructed to take the medication at the onset of their next migraine and to notice if the pain of their migraine felt reduced after half an hour. Fifty patients receiving the new treatment reported reduced pain, compared with only 40 of the patients receiving the standard treatment. The results seem to favor the new treatment, but could the difference just be due to chance? In this problem, consider the null hypothesis that the percentage of patients with a reduction in pain is the same between the two treatments, versus the alternative hypothesis that the percentages are different. (a) Under the null hypothesis, the difference in the sample percentages is expected to be ___%. The standard error for the difference is estimated to be ___%. (b) Calculate…
A researcher is creating a new treatment protocol for Myelodysplastic Syndrome (MDS), a form of preleukemia. Following the old treatment protocol, 28% of patients with MDS will develop leukemia within 5 years of MDS diagnosis. He believes his new treatment protocol will lead to fewer MDS patients developing leukemia. He takes a random sample of 100 individuals on his new treatment protocol. Of these 100 individuals, 20 develop leukemia within 5 years of MDS diagnosis. In questions 8-9, create a 98% confidence interval for the true proportion of all MDS patients on this new treatment who will develop leukemia within 5 years of MDS diagnosis. What is the confidence interval? Do not round your answer. What is the interpretation of your confidence interval?
A researcher took a random sample of 200 new mothers in the United States (Group 1) and found that 16% of them experienced some form of postpartum depression. Another random sample of 200 new mothers in France (Group 2), where mothers receive 16 weeks of paid maternity leave, found that 11% experienced some form of postpartum depression. Can it be concluded that the percent of women in the United States experience more postpartum depression than the percent of women in France? Use α=0.05. Select the correct alternative hypothesis and decision
With two COVID-19 vaccines now in the final stages of approval for use in the U.S., 63% of Americans say they are willing to receive a COVID-19 vaccination approved by the Food and Drug Administration (FDA), up from 50% who said this in September. The December results came from a Gallup poll conducted Nov. 16-29, 2020, with a random sample of 2,968 adults. The September results came from a Gallup poll conducted Sept. 14-27, 2020, with a random sample of 2,730 adults. Does this data suggest that the share of Americans who say they plan to get vaccinated has increased? State and test the relevant hypotheses at significance level 0.10 by using the P-value method.
A researcher is creating a new treatment protocol for Myelodysplastic Syndrome (MDS), a form of preleukemia. Following the old treatment protocol, 28% of patients with MDS will develop leukemia within 5 years of MDS diagnosis. He believes his new treatment protocol will lead to fewer MDS patients developing leukemia. He takes a random sample of 100 individuals on his new treatment protocol. Of these 100 individuals, 20 develop leukemia within 5 years of MDS diagnosis. Conduct a hypothesis test at the 10% level to test this claim that his new treatment protocol will lead to fewer MDS patients developing leukemia. What is the appropriate conclusion/interpretation for this hypothesis test? Write a few sentences.