Pregnancy Test A pregnancy testing device is used by 1000 different women from a
ID: 3297604 • Letter: P
Question
Pregnancy Test
A pregnancy testing device is used by 1000 different women from a population of women who think they might be pregnant. The results are depicted in the contingency table below.
Here, a positive pregnancy test result means pregnancy is detected.
Was the Woman Actually Pregnant?
Yes
No
Positive Test Result
479
13
Negative Test Result
6
502
Question 5:
Suppose you are a woman who takes the test and it comes back negative. What is the probability that the test result is wrong, i.e. that the test result is negative but you are actually in fact pregnant?
(Hint: This is a conditional probability problem. You are restricted to only considering the test results that came back negative.)
Why is the probability of getting a false negative about twice as high for those who have already obtained a negative test result versus those who have not yet taken the test?
Was the Woman Actually Pregnant?
Yes
No
Positive Test Result
479
13
Negative Test Result
6
502
Explanation / Answer
From the above given information we can find the probability that the test result is wrong, i.e. that the test result is negative but you are actually in fact pregnant
= Pr( test result is negative given that women is pregnant)
= Pr( test result is negative and women is pregnant) / Pr( women is pregnant)
= 6/485
= 0.01237