Question

A rheumatologist wants to determine if a new brand of tests is effective in detecting whether or not a patient has food allergies. Use the table below to determine the probability of a false negative given a NEGATIVE Test result. Enter your answer as a simplified fraction. Disease No Disease Total Positive Test 40 6 46 Negative Test 2 78 80 Total 42 84 126

Answer 1

The probability of a false negative given a NEGATIVE Test result is 1/40, derived from the ratio of false negatives to total patients and negative test results.

To determine the probability of a false negative given a NEGATIVE Test result, you need to use the formula:

P(False Negative | NEGATIVE Test) = P(False Negative ∩ NEGATIVE Test) / P(NEGATIVE Test)

Using the table, you can find the values of the probabilities as follows:

P(False Negative ∩ NEGATIVE Test) is the number of false negatives divided by the total number of patients. In this case, there are 2 false negatives out of 126 patients, so the probability is 2/126.

P(NEGATIVE Test) is the number of negative test results divided by the total number of patients. In this case, there are 80 negative test results out of 126 patients, so the probability is 80/126.

Plugging these values into the formula, you get:

P(False Negative | NEGATIVE Test) = (2/126) / (80/126) = 2/80 = 1/40

Therefore, the probability of a false negative given a NEGATIVE Test result is 1/40. This is the answer in simplified fraction form.