4. ) A clinic\'s test for the flu results in 5% of patients testing positive. Th

ID: 3355522 • Letter: 4

Question

4. ) A clinic's test for the flu results in 5% of patients testing positive. The medical supply company behind this

test claims that 90% of patients who test positive for flu actually have the disease, and 15% of patients testing negative

also have the flu. What is the probability that a patient being tested for flu actually has the disease?

Using the following probability tree, calculate the probability of a patient actually having the flu, P(flu) = ?

Flu, 0.90

Positive, 0.05 No Flu, 0.10

Negative, 0.95 Flu, 0.15

No Flu, 0.85

Let Flu, No Flu, positive, negetive be denoted by F, NF, +ve and -ve respectively

P(+ve) = 0.05, P(-ve) = 0.95

P(F|+ve) = 0.9, P(NF|+ve) = 0.1

P(F|-ve) = 0.15, P(NF|-ve) = 0.85

P(F) = (P(F|+ve) * P(+ve)) + (P(F|-ve) * P(-ve))

P(F) = (0.9 * 0.05) + (0.15 * 0.95)

P(F) = 0.045 + 0.1425 = 0.147

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