A website for home pregnancy test cites the following: “When the subjects using

Question

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 sensitivity1 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?

Explanation / Answer

let Po is event that test gives +ve result

let Ne is event that test gives -ve result

A is event that women is actual pregnant

B is event that women is not in actual pregnant

P(A) =0.30

P(B) =0.70

P(Po |A) =0.75

P(Ne|A)=0.25

P(Ne|B) =0.52 P(Po|B) =0.48

we have to find P(A|Po)=?

now

P(A|Po)=(P(Po|A)P(A))/P(Po)

=(P(Po|A)P(A)) /( P(Po|A)P(A)+P(P0|B)P(B))

=(0.75*0.3)/(0.75*0.3+0.48*0.7)

=0.225/(0.225+0.336)

=0.225/0.561

=0.401

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