2020 statistics show that 50% of women age 20 and younger have taken a pregnancy test and 30% of those who have taken a pregnancy test are or have been pregnant. Over the counter pregnancy tests give a false positive 5% of the time and a false negative 13% of the time.
1). Assuming that none of the women who did not take a pregnancy test were pregnant, what percentage of women age 20 and under are or have been pregnant?
2) Given that a woman took a pregnancy test, what is the probability that she had a false negative test?
3) For a woman who received a negative pregnancy test, what is the probability she actually was pregnant?
4) For a woman who received a positive pregnancy test, what is the probability that she was not pregnant?
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1) To find the percentage of women age 20 and under who are or have been pregnant, we can use the information provided in the statistics. We know that 50% of women age 20 and younger have taken a pregnancy test, and 30% of those who have taken a pregnancy test are or have been pregnant.
First, we find the percentage of women who have taken a pregnancy test and are or have been pregnant. This can be calculated by multiplying the percentage of women who have taken a pregnancy test (50%) by the percentage of those who have taken a pregnancy test and are or have been pregnant (30%):
(50% * 30%) = 15%
Therefore, 15% of women age 20 and under are or have been pregnant.
2) To find the probability that a woman had a false negative test given that she took a pregnancy test, we need to use the information given regarding the false negative rate. We know that over-the-counter pregnancy tests give a false negative result 13% of the time.
Therefore, the probability of having a false negative test is 13%.
3) To find the probability that a woman who received a negative pregnancy test was actually pregnant, we need to use information about false negative and false positive rates. We know that over-the-counter pregnancy tests give a false negative result 13% of the time.
To calculate the probability, we can subtract the false negative rate from 100% since a negative test result means not being pregnant (assuming none of those who did not take a test were pregnant):
100% - 13% = 87%
Therefore, there is an 87% probability that a woman who received a negative pregnancy test was actually not pregnant.
4) To find the probability that a woman who received a positive pregnancy test was not pregnant, we need to use the false positive rate. We know that over-the-counter pregnancy tests give a false positive result 5% of the time.
Therefore, the probability of a false positive test is 5%.
Hence, the probability that a woman who received a positive pregnancy test was not actually pregnant is 5%.