A study looked at the effectiveness of an x-ray screening test for tuberculosis

Question

A study looked at the effectiveness of an x-ray screening test for tuberculosis with 1820 subjects, 30 with tuberculosis and 1790 without. The test gave an outcome of 'Negative' (does not have tuberculosis) or 'Positive' (has tuberculosis), with the results shown in the following table: Tuberculosis X-Ray Negative 1739 Positive Total No Yes Total 81747 51 22 73 1790 30 1820 Use these results to estimate the sensitivity and specificity of this x-ray screening test. Suppose this screening test will now be used for a population where the prevalence of tuberculosis is 9.3 in 100,000. Based on this study, what is the probability someone has tuberculosis if they receive a positive x-ray result? a) 0.0024 b) 0.0285 c) 0.1486 d) 0.3014 e) 0.7333

Explanation / Answer

Solution:

Here we will use conditional probability rather than joint probability

So p(some one have tuberculosis if they have receive a positive x ray result)

= P(Tuberculosis and positive x ray result)/P(positive x ray result)

= 22/73 = 0.301369863

So its answer is D. I.e. 0.3014

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.