Pregnancy Test A pregnancy testing device is used by 1000 different women from a
ID: 3062690 • 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 1:
Using the relative frequency approximation of probabilities, what is the probability that the device is correct?
(Hint: remember that a correct result occurs when both the pregnancy test result is positive when the women is actually pregnant AND when the pregnancy test result is negative when the women is actually not pregnant.)
Question 2:
Suppose you are a woman about to take the test. Prior to taking the test, what is the probability of a false positive? In other words, how many of the 1000 tests will produce a positive test result when the woman is not actually pregnant?
Question 3:
Suppose you are a woman who takes the test and it comes back positive. What is the probability that the test result is wrong, i.e. that the test result is positive but you are not actually pregnant?
(Hint: This is a conditional probability problem. You are restricted to only considering the test results that came back positive.)
Why is the probability of getting a false positive about twice as high for those who have already obtained a positive test result versus those who have not yet taken the test?
Question 4:
Suppose you are a woman about to take the test. Prior to taking the test, what is the probability of a false negative? In other words, how many of the 1000 tests will produce a negative test result when the woman is actually in fact pregnant?
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
1) P(device is correct) = P(pregnant and positive result) + P(not pregnant and negative result)
= (479+502)/1000
= 0.981
2) P(false positive) = 13/1000
= 0.013
3) P(test is wrong when came back positive) = Number of cases with wrong positives/Total number of positives
= 13/(479+13)
= 0.026
The probability of getting a false positive about twice as high for those who have already obtained a positive test result versus those who have not yet taken the test because the value in denominator have become almost half. Before taking test, we have to consider the whole 1000 people, but after test, we do not have to consider the 508 people who got negative test result.
4) P(false negative) = 6/1000 = 0.006
5) P(test is wrong when the result is negative) = P(test is wrong and result is negative)/ P(result is negative)
= 6/(6+502)
= 0.012
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 because after the test we need not consider the part of the population that had positive result. So, the denominator is almost halved and hence the probability is doubled.