Test for TBTB absentTB presentNegative17398Positive5122Data for TB testing using X-ray imagingTable shows the results of using X-ray imaging as a diagnostic test for tuberculosis in patients withknown TB status. Use it to answer the questions below.1. Calculate the marginal probabilities of the individual random variables, i.e. the probability of positiveand negative X-ray test results, and of TB being present and absent.2. Find the probability of positive result given that TB is absent (false positive rate) and the probabilityof a negative result given that TB is absent (specificity).3. Find the probability of negative result given that TB is present (false negative rate) and theprobability of a positive result given that TB is present (sensitivity).4. Find the probability that a person who tests positive actually has TB (probability of TB present givena positive result).5. Find the probability that a person who tests negative does not have TB (probability of no TB given anegative result).6. Assuming the test result and the TB status are independent, calculate the expected probability ofboth TB being present and a positive X-ray test.}7. Under the same assumption, calculate the expected probability of both TB being absent and apositive X-ray test.

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Data for TB testing using X-ray imaging

A First Course in Probability (10th Edition)

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ISBN:9780134753119

Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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Question

Test for TB
TB absent
TB present
Negative
1739
8
Positive
51
22
Data for TB testing using X-ray imaging
Table shows the results of using X-ray imaging as a diagnostic test for tuberculosis in patients with
known TB status. Use it to answer the questions below.
1. Calculate the marginal probabilities of the individual random variables, i.e. the probability of positive
and negative X-ray test results, and of TB being present and absent.
2. Find the probability of positive result given that TB is absent (false positive rate) and the probability
of a negative result given that TB is absent (specificity).
3. Find the probability of negative result given that TB is present (false negative rate) and the
probability of a positive result given that TB is present (sensitivity).
4. Find the probability that a person who tests positive actually has TB (probability of TB present given
a positive result).
5. Find the probability that a person who tests negative does not have TB (probability of no TB given a
negative result).
6. Assuming the test result and the TB status are independent, calculate the expected probability of
both TB being present and a positive X-ray test.}
7. Under the same assumption, calculate the expected probability of both TB being absent and a
positive X-ray test.

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