Biostatistics/biostats and Bayes Theorm and Conditional Probability A test has r

Question

Biostatistics/biostats and Bayes Theorm and Conditional Probability

A test has recently been developed for Swine flu (H1N1 virus) that can be given to travellers returning to the US from other countries. Like all medical tests, this test is not perfect. During one of the initial trials of the test, 1000 individuals from Mexico were tested. Of those tested, 10 had swine flu but tested negative (false negative), 60 had swine flu and tested positive, and 30 did not have swine flu but tested positive (false positive). The remaining 900 individuals did not have swine flu and tested negative. a. Write out the following probabilities: I. P[+ test|Flu] =

II. P[- test|Flu] =

III. P[+ test| no Flu] =

IV. P[- test|no Flu] =

b. If a traveller returning to the US from Mexico tests positive for swine flu, what is the probability that s/he actually has the virus?

Bayes Therom

Conditional Probability

Explanation / Answer

a. I. P[+ test|Flu] =60 / (60+10) = 6/7 = 0.8572

II. P[- test|Flu] =(10)/(10+60) = 1/7 = 0.1428

III. P[+ test| no Flu] = 30/(30+900) = 0.0323

IV. P[- test|no Flu] =900/(900+30) = 0.9677

b. P(Flu | + test) = P[+ test|Flu] * P(Flu) / [ P[+ test|Flu] * P(Flu) + P(+ test | no flu) * P(no flu) ]

= 0.8572 * (10+60)/1000 / [0.8572 * (10+60)/1000 + 0.0323*(900+30)/1000] = 60/90 = 2/3 = 0.6667

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