A 2020 statistics shows 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?
1) To find the percentage of women age 20 and under who are or have been pregnant, we need to consider two groups: those who have taken a pregnancy test and those who have not.
Since the statistics provided only pertain to women who have taken a pregnancy test, we need to calculate the percentage of women who have not taken a test and are not pregnant (assuming none of them are pregnant).
Let's assume there are 100 women age 20 and under in total. If 50% of them have taken a pregnancy test, that means 50 women have taken a test and the other 50 women have not.
Out of the 50 women who took a test, 30% of them are or have been pregnant. That is 30% of 50, which is 0.3 * 50 = 15 women.
Thus, the number of women age 20 and under who are or have been pregnant is 15.
Now, out of the 50 women who did not take a pregnancy test, we assumed that none of them are pregnant, so the number of pregnant women in that group is 0.
Therefore, the total number of pregnant women out of the 100 women age 20 and under is 15 + 0 = 15.
To calculate the percentage, we divide 15 (number of pregnant women) by 100 (total number of women) and multiply by 100 to get the percentage: (15/100) * 100 = 15%.
So, assuming none of the women who did not take a pregnancy test were pregnant, the percentage of women age 20 and under who are or have been pregnant is 15%.
2) Given that a woman took a pregnancy test, we need to find the probability that she had a false negative. A false negative means the test shows negative (not pregnant) when the woman is actually pregnant.
To calculate this probability, we need to find the ratio of false negative tests to the total number of tests.
The false negative rate is given as 13%, which means 13% of the tests give a false negative. So, the probability of a false negative is 13%.
Therefore, the probability that a woman had a false negative test, given that she took a pregnancy test, is 13%.
3) We want to find the probability that a woman was actually pregnant, given that she received a negative pregnancy test result.
To calculate this, we need to consider both true negative results (the test correctly indicates "not pregnant") and false negative results (the test incorrectly indicates "not pregnant" when the woman is actually pregnant).
Since we have the false negative rate as 13%, we also know the true negative rate (the complement of the false negative rate) is 100% - 13% = 87%.
The probability of a woman receiving a negative pregnancy test result but actually being pregnant is equal to the false negative rate divided by the sum of the false negative rate and true negative rate.
So, the probability that a woman who received a negative pregnancy test result is actually pregnant is 13% / (13% + 87%) = 13% / 100% = 13%.
Therefore, the probability that a woman who received a negative pregnancy test result was actually pregnant is 13%.
4) We want to find the probability that a woman who received a positive pregnancy test result was not actually pregnant.
To calculate this, we need to consider both true positive results (the test correctly indicates "pregnant") and false positive results (the test incorrectly indicates "pregnant" when the woman is not actually pregnant).
The false positive rate is given as 5%, which means 5% of the tests give a false positive. So, the probability of a false positive is 5%.
Therefore, the probability that a woman who received a positive pregnancy test result was not actually pregnant is 5%.