A seasonal viral infection due to a virus named RandomV is prevalent in Delhi. About 1...
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A seasonal viral infection due to a virus named RandomV is prevalent in Delhi. About 1 in 1000 people in Delhi are expected to be infected by RandomV. The virus spreads from an infected person to another person only when a sufficient amount of viral load is transmitted from the infected person to the other. A test has been designed to detect the RandomV infection. Among the infected, the test gives a positive result in 90% of them. Among healthy people (that is those who are free of infection), the test is known to come up with a positive result in 10% of them. Given the above background about RandomV, solve the following questions. Question 1. Suppose you go to a gathering of 10 people who have come together from different parts of Delhi to celebrate Delhi's history. Derive the following probabilities. (a) You meet a randomly chosen person in the gathering. What is the probability that the person is infected with Random V? (b) You meet a randomly chosen pair in the gathering. What is the probability that you end up meeting a pair of infected people? (c) You meet a randomly chosen pair in the gathering. What is the probability that you end up meeting a pair in which one or more are infected? (d) What is the probability that two or more in the gathering of 10 are infected? Question 2. Knowing the infectious nature of RandomV, a certain healthy person decides to limit his daily interaction with other people. However, given the person's work, he ends up meeting a total of two people on a certain day. He does not know whether the two people were infected. However, he has read that an infected person can with probability 0.1 transfer a viral load that is sufficient to infect a healthy person. Also, for a given healthy person, the outcomes of interactions with different infected people are independent of each other. The person is worried post his meetings with the two people and decides to get himself tested. (a) Derive the probability that his test will give a positive result. [Hint: What is the probability that the person is infected?] (b) Suppose his test gives a positive result. What is the probability that the person is infected with RandomV? Question 3. Consider the person in Question 2 and his meeting two people on his work day. Now suppose that a vaccine exists to protect against RandomV. The vaccine is known to have an efficacy of 95%, which is to say that the probability that an infected person transfers a viral load that is sufficient to infect a healthy vaccinated person is 1/20 of the corresponding probability for a healthy unvaccinated person. It is also known that the behavior of the test is independent of whether a person is vaccinated or not. What is the probability that the above person is vaccinated, given that his test result is positive? [Hint 1: Note that for events A, B, and C, P[A, BIC] = P[AB, CP[BC]. Hint 2: The probability that the person is infected, given that he is vaccinated, may be useful.]. A seasonal viral infection due to a virus named RandomV is prevalent in Delhi. About 1 in 1000 people in Delhi are expected to be infected by RandomV. The virus spreads from an infected person to another person only when a sufficient amount of viral load is transmitted from the infected person to the other. A test has been designed to detect the RandomV infection. Among the infected, the test gives a positive result in 90% of them. Among healthy people (that is those who are free of infection), the test is known to come up with a positive result in 10% of them. Given the above background about RandomV, solve the following questions. Question 1. Suppose you go to a gathering of 10 people who have come together from different parts of Delhi to celebrate Delhi's history. Derive the following probabilities. (a) You meet a randomly chosen person in the gathering. What is the probability that the person is infected with Random V? (b) You meet a randomly chosen pair in the gathering. What is the probability that you end up meeting a pair of infected people? (c) You meet a randomly chosen pair in the gathering. What is the probability that you end up meeting a pair in which one or more are infected? (d) What is the probability that two or more in the gathering of 10 are infected? Question 2. Knowing the infectious nature of RandomV, a certain healthy person decides to limit his daily interaction with other people. However, given the person's work, he ends up meeting a total of two people on a certain day. He does not know whether the two people were infected. However, he has read that an infected person can with probability 0.1 transfer a viral load that is sufficient to infect a healthy person. Also, for a given healthy person, the outcomes of interactions with different infected people are independent of each other. The person is worried post his meetings with the two people and decides to get himself tested. (a) Derive the probability that his test will give a positive result. [Hint: What is the probability that the person is infected?] (b) Suppose his test gives a positive result. What is the probability that the person is infected with RandomV? Question 3. Consider the person in Question 2 and his meeting two people on his work day. Now suppose that a vaccine exists to protect against RandomV. The vaccine is known to have an efficacy of 95%, which is to say that the probability that an infected person transfers a viral load that is sufficient to infect a healthy vaccinated person is 1/20 of the corresponding probability for a healthy unvaccinated person. It is also known that the behavior of the test is independent of whether a person is vaccinated or not. What is the probability that the above person is vaccinated, given that his test result is positive? [Hint 1: Note that for events A, B, and C, P[A, BIC] = P[AB, CP[BC]. Hint 2: The probability that the person is infected, given that he is vaccinated, may be useful.].
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Question 1 a Probability of meeting an infected person Given that 1 in 1000 people in Delhi are infe... View the full answer
Related Book For
Molecular Cell Biology
ISBN: 978-1429234139
7th edition
Authors: Harvey Lodish, Arnold Berk, Chris A. Kaiser, Monty Krieger, Anthony Bretscher, Hidde Ploegh, Angelika Amon, Matthew P. Scott
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