Question

1. refer to the table which summarizes the results of testing for a certain disease.

| positive test result negative test result
subject has the disease \t111 \t4
subject does not have the disease\t11 \t172
if one of the results is randomly selected, what is the probability that it is a false negative (test indicates the person does not have the disease when in fact they do)? what does this probability suggest about the accuracy of the test?
a) 0.0369; the probability of this error is low so the test is fairly accurate.
b) 0.0134; the probability of this error is low so the test is fairly accurate.
c) 0.0348; the probability of this error is low so the test is fairly accurate.
d) 0.591; the probability of this error is high so the test is not very accurate.
estimate the probability of the event.

Explanation:

Step1: Identify false negative cases

False negative is when subject has disease but test is negative. From table, that's 4.

Step2: Calculate total number of test results

Total = (111 + 4) + (11 + 172) = 115 + 183 = 298.

Step3: Compute probability of false negative

Probability = $\frac{\text{False Negative}}{\text{Total}}$ = $\frac{4}{298}$ ≈ 0.0134? Wait, no, wait: Wait, subject has disease: 111 (positive) + 4 (negative) = 115. Wait, total test results: 111 + 4 + 11 + 172 = 298? Wait, 111+4=115, 11+172=183, 115+183=298. Wait, false negative is 4 (subject has disease, test negative). So probability is 4 / (111 + 4) ? Wait no, wait the question is "if one of the results is randomly selected", so total results are all four cells: 111,4,11,172. So total is 111+4+11+172=298. False negative is 4 (subject has disease, test negative). So probability is 4 / 298 ≈ 0.0134? Wait but let's recalculate: 111+4=115 (has disease), 11+172=183 (no disease). Total 115+183=298. False negative: 4 (has disease, negative test). So 4/298 ≈ 0.0134? Wait but option C is 0.0348, option A is 0.0369, B is 0.0134. Wait maybe I made a mistake. Wait, false negative: subject has disease, test negative. So number of false negatives is 4. Number of subjects with disease is 111 + 4 = 115. Wait, is the probability conditional? Wait the question says "if one of the results is randomly selected", so it's the probability that a randomly selected result is a false negative. So false negative is 4, total results is 111 + 4 + 11 + 172 = 298. So 4/298 ≈ 0.0134, which is option B? Wait but let's check again. Wait 111 (true positive), 4 (false negative), 11 (false positive), 172 (true negative). So total test results: 111 + 4 + 11 + 172 = 298. False negative: 4. So 4/298 ≈ 0.0134. So the probability is approximately 0.0134, and since this error probability is low, the test is fairly accurate. So option B.

Answer:

B. 0.0134; The probability of this error is low so the test is fairly accurate.