Question

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Problem 6 A website for home pregnancy test cites the following: "When the subjects using the test were women who collected and tested their own samples, the overall sensitivityl was 75%. The specificity2 was 52%. Suppose a subject has a positive test and that 30% of women taking pregnancy tests are actually pregnant. [1] Sensitivity: probability that the test is positive given that the subject is pregnant. [2] Specificity: probability that the test is negative given that the subject is not pregnant. What is the probability of pregnancy given a positive test?

Answer 1

TOPIC:Application of the Bayes' theorem.

Prooblem - 6% Define the following events as L T : CP: The test is positive; The subject is pregnant. Given that, ay sensitivity = 0.75 (in decimals). I P The test is positive = 0.75. er the subject is pregnant YP (TIP) = 0.75 Again, → Specificity = 0.52 (in decimals. P (The test is / The subject is). I l negative not pregnant =0.52, > [T4787 +0:52 Law of 2) P (TIP c) = 1- P (Telpc). I co comblemen tation 21-0.52. 20.48.

Again, P (of being actually pregnant) = 30 = 0.30 XP (P) = 0.30. I Law of comple- mentation) -P(P) = 1-0.30 = 0.70. We need to find nel The subject is / The test is I pregnant I positive =P(PIT). P(P). P (T/P) P(P). P(TIP) +P(p). P(T/P9) Bayes' theorem 0.30 x 0.75 0.30x0.75 +0. Jo x By the given a results 0.48 0.4011 (in Jour decimals) (And]