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VI) Bayes' Theorem [10 points] The PCR test for COVID-19 has a sensitivity of $P(T+|D+) = 0.99$ and a specificity of $P(T-|D-) = 0.98$ where $D+$ is the event that an individual is infected, $T+$ is the event that their PCR test comes back positive, and $D^-$ and $T^-$ are the complements of these. (a) At the beginning of the pandemic the infection was rare with $P(D+) = 0.001$. If a randomly chosen individual's PCR test comes back positive, what is the probability that they are actually infected? (b) You might recall that in the early stages of the pandemic, when the infection was rare, only people who displayed symptoms were tested. Suppose that, among those individuals displaying symptoms, $P(D+) = 0.1$. If a randomly chosen symptomatic individual's PCR test comes back positive, what is the probability that they are actually infected?

Name: vi bayes theorem 10 points the pcr test for covid 19 has a sensitivity of ptd 099 and a specificity of pt d 098 where d is the event that an individual is infected t is the event that their 92177
Uploaded: 2024-09-18T20:37:33-08:00
Duration: 2 min 43 s
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Description: vi bayes theorem 10 points the pcr test for covid 19 has a sensitivity of ptd 099 and a specificity of pt d 098 where d is the event that an individual is infected t is the event that their 92177

          VI) Bayes' Theorem [10 points] The PCR test for COVID-19 has a sensitivity of $P(T+|D+) = 0.99$ and a specificity of $P(T-|D-) = 0.98$ where $D+$ is the event that an individual is infected, $T+$ is the event that their PCR test comes back positive, and $D^-$ and $T^-$ are the complements of these.
(a) At the beginning of the pandemic the infection was rare with $P(D+) = 0.001$. If a randomly chosen individual's PCR test comes back positive, what is the probability that they are actually infected?
(b) You might recall that in the early stages of the pandemic, when the infection was rare, only people who displayed symptoms were tested. Suppose that, among those individuals displaying symptoms, $P(D+) = 0.1$. If a randomly chosen symptomatic individual's PCR test comes back positive, what is the probability that they are actually infected?

vi bayes theorem 10 points the pcr test for covid 19 has a sensitivity of ptd 099 and a specificity of pt d 098 where d is the event that an individual is infected t is the event that their 92177

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