In a city of 1000 residents, 50 of them have been diagnosed with COVID-19. Among the COVID-19 patients, 78% had fever, 57% got coughing symptom, and 25% experienced loss of smell. The symptoms are conditionally independent for the COVID-19 patients. For all the residents that did not contract the COVID-19 virus, 15% experienced coughing symptom and none of them have other symptoms. (i) What is the probability that a resident contracted COVID-19, and experienced both fever and loss of smell symptoms? (ii) Given that a resident experienced coughing symptom, what is the probability that the resident has contracted the COVID-19 virus?

In a city of 1000 residents, 50 of them have been diagnosed with COVID-19. Among the COVID-19 patients, 78% had fever, 57% got coughing symptom, and 25% experienced loss of smell. The symptoms are conditionally independent for the COVID-19 patients. For all the residents that did not contract the COVID-19 virus, 15% experienced coughing symptom and none of them have other symptoms. (i) What is the probability that a resident contracted COVID-19, and experienced both fever and loss of smell symptoms? (ii) Given that a resident experienced coughing symptom, what is the probability that the resident has contracted the COVID-19 virus?

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

Of the people in Canada, 44% have received two doses of Covid-19 vaccine, 38% have received onedose of Covid-19 vaccine, and the remainder have not received any dose of Covid-19 vaccine. Notethat the level of risk for Covid-19 infection are high and low risks. Of those who have received twodoses of Covid-19 vaccine, 8% are at high risk for Covid-19 infection, whereas 20% of those who havereceived one dose of Covid-19 vaccine and 60% of those who have not received any dose of Covid-19vaccine are at high risk for Covid-19 infection. Suppose that we randomly select one person inCanada. What is the probability that the persona) is at low risk for Covid-19 infection, given that person has received two doses of Covid-19 vaccine?b) is at low risk for Covid-19 infection?c) do not receive any dose of Covid-19 vaccine, given that that person is at low risk for Covid-19infection
The manufacturer of the ColorSmart-5000 television set claims that 95 percent of its sets last at least five years without needing a single repair. In order to test this claim, a consumer group randomly selects 400 consumers who have owned a ColorSmart-5000 television set for five years. Of these 400 consumers, 316 say that their ColorSmart-5000 television sets did not need repair, while 84 say that their ColorSmart-5000 television sets did need at least one repair. Formulate the null and alterative hypotheses that the consumer group should use to attempt to show that the manufacturer’s claim is false. Use the critical value approach to test the hypotheses by setting α equal to 0.10 and 0.001.
In the current pandemic, researchers are working on creating antibody tests to determine which individuals have already had an infection caused by the COVID-19 virus. If someone has been infected, then they will have certain antibodies in their system and the hope is that a highly accurate test can be created to detect these antibodies. Assume a researcher creates a new antibody test, which for individuals who are known to have had the infection in the past and thus truly have the COVID-19 antibodies, gives a positive result 95% of the time. This same test gives a negative result 90% of time for people who do not have the antibodies. Assume that COVID-19 has affected 5% of the population in the region of interest. What is the probability someone has NOT been infected previously given that their antibody test result comes back positive? [four decimals]
In a study of pain relievers, 25 people were given product A, and all but 7 experienced relief. In the same study, 100 people were given product B, and all but 20 experienced relief. Fill in the blanks below to make the most reasonable statement possible. Product A or B performed better in the study. That is because only ____ % failed to get relief with this product, whereas _______% failed to get relief with Product A or B
In a double round robin Basketball games composed of 8 teams, team A was able to win over 3 teams. In the second round, what is theprobability of team A winning a game.
Suppose a survey was done in three states on the Covid-19 pandemic situation. Of the total population of the three states, 25% live in state X, 45% live in state Y, and 30% live in state Z. In state X, 20% of the citizens have been infected with Covid-19, in state B, 10% of the citizens have been infected with Covid-19, and in state C, 15% of the citizens have been infected with Covid-19. Let X represents the event that the citizen is from state X, Y represents the event that the citizen is from state Y and Z represents the event that the citizen is from state Z. Let C represents the event that the citizen has been infected with Covid-19. a) Find the probability that a randomly selected citizen has not been infected with Covid-19 and lives in state X and find the probability that a randomly selected citizen has been infected with Covid-19 and Given that a randomly selected citizen has been infected with Covid-19, find the probability that the selected citizen is from state Y.
A political strategist claims that 58% of voters in Madison County support his candidate. In a poll of 500 randomly selected voters, 260 of them support the strategist's candidate. At alpha = .05, is the political strategist's claim warranted?
In a recent study, 20 males used a new weight-loss supplement, and 14 of them experienced weight loss after two weeks. In the same study, 50 females used the same supplement, and 29 of them experienced weight loss after two weeks. Fill in the blanks below to make the most reasonable statement possible. The new weight-loss supplement was less effective on ▼(Choose one) in the study. That is because % of them failed to lose weight after two weeks, whereas only % of the ▼(Choose one) failed to lose weight after two weeks.
A pharmaceutical company claims that after the clinical trials, it will release the first-ever cure for COVID-19. If they have committed an error of judgement, which type of error would they rather have, Type I or Type II? Why?
In a recent study, 25 males used a new weight-loss supplement, and all but 7 of them experienced weight loss after two weeks. In the same study, 100 females used the same supplement, and all but 45 of them experienced weight loss after two weeks. Fill in the blanks below to make the most reasonable statement possible. The new weight-loss supplement was more effective on ▼(Choose one) in the study. That is because _% of them lost weight after two weeks, whereas only _% of the ▼(Choose one) lost weight after two weeks.
3. On Feb 25, 2021, there were 461,058 new cases of COVID reported in the world, 77803 in the US, and 512 in Oregon. On that same day, 11493 people died worldwide of COVID, 2465 in the US, and 10 died in Oregon from COVID. The world population is 7.9 billion, the US population is 331.42 million, and Oregon has 4.32 million residents. fill in blanks, show work. Compared to the world, Oregon had ____ % of the cases, but _____% of the deaths and ______ % of the world population.
In a recent study, 20 males used a new weight-loss supplement, and 14 of them experienced weight loss after two weeks. In the same study, 100 females used the same supplement, and 82 of them experienced weight loss after two weeks. Fill in the blanks below to make the most reasonable statement possible. The new weight-loss supplement was more effective on ▼(Choose one) in the study. That is because only % of them failed to lose weight after two weeks, whereas % of the ▼(Choose one) failed to lose weight after two weeks.