Consider a test whether a person is infected with a virus or not. Assume that a rate x of people infected with the virus

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Consider a test whether a person is infected with a virus or not. Assume that a rate x of people infected with the virus

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Consider A Test Whether A Person Is Infected With A Virus Or Not Assume That A Rate X Of People Infected With The Virus 1
Consider A Test Whether A Person Is Infected With A Virus Or Not Assume That A Rate X Of People Infected With The Virus 1 (99.79 KiB) Viewed 29 times
Consider a test whether a person is infected with a virus or not. Assume that a rate x of people infected with the virus in the community is x=0.001 and a prior probability that a person in the community is infected with the virus is equal to x. In addition, y is a probability that an infected person tests positive and z is a probability that a non-infected person erroneously tests positive. Answer the following questions. 1. Assume that y=0.8 and z=0.001. Find a probability that a person is actually infected with the virus when the person tests positive. 2. Let the relationship between y and z be z=0.001y2+0.0005(0≤y≤1). Find y that maximizes the probability that a person is actually infected with the virus when the person tests positive.
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