3. Bayes' Theorem. On September 2nd the previous week n=35,000 Covid-19 tests were performed. After double checking it was confirmed that of these, T=175 students had the virus. That is, P(T)=0.005. The test Student Health sent a letter informing that in swabs used had a 98% sensitivity, that is the probability of designating an infected individual as positive, P(+|T). Also the tests has a 99% specificity, that is the probability of designating a healthy individual as negative, P(-|F). Suppose that during that week you took a single test and you resulted positive (+), what are the odds that you were a false positive? Find P(F|+) and show your work with a tree diagram.
3. Bayes' Theorem. On September 2nd the previous week n=35,000 Covid-19 tests were performed. After double checking it was confirmed that of these, T=175 students had the virus. That is, P(T)=0.005. The test Student Health sent a letter informing that in swabs used had a 98% sensitivity, that is the probability of designating an infected individual as positive, P(+|T). Also the tests has a 99% specificity, that is the probability of designating a healthy individual as negative, P(-|F). Suppose that during that week you took a single test and you resulted positive (+), what are the odds that you were a false positive? Find P(F|+) and show your work with a tree diagram.
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![3. Bayes' Theorem. On September 2nd
the previous week n=35,000 Covid-19 tests were performed. After double checking it
was confirmed that of these, T=175 students had the virus. That is, P(T)=0.005. The test
Student Health sent a letter informing that in
swabs used had a 98% sensitivity, that is the probability of designating an infected
individual as positive, P(+|T). Also the tests has a 99% specificity, that is the probability
of designating a healthy individual as negative, P(-|F). Suppose that during that week
you took a single test and you resulted positive (+), what are the odds that you were a
false positive? Find P(F|+) and show your work with a tree diagram.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0956cf0b-5906-4b5a-a0f4-bc627eb69e8e%2F6d15e6b1-5ce6-4163-bd45-ef48d1e4b340%2Frcayuiu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Bayes' Theorem. On September 2nd
the previous week n=35,000 Covid-19 tests were performed. After double checking it
was confirmed that of these, T=175 students had the virus. That is, P(T)=0.005. The test
Student Health sent a letter informing that in
swabs used had a 98% sensitivity, that is the probability of designating an infected
individual as positive, P(+|T). Also the tests has a 99% specificity, that is the probability
of designating a healthy individual as negative, P(-|F). Suppose that during that week
you took a single test and you resulted positive (+), what are the odds that you were a
false positive? Find P(F|+) and show your work with a tree diagram.
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