Thank you in advance
In a 2020 statistic 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?
To answer these questions, we can use conditional probability. Conditional probability is the probability of an event occurring given that another event has already occurred. Let's use the given information to find the answers to each question:
1) Assuming that none of the women who did not take a pregnancy test were pregnant, we can calculate the percentage of women age 20 and under who are or have been pregnant.
First, let's find the percentage of women who have taken a pregnancy test: 50% of women age 20 and younger have taken a pregnancy test.
Next, let's find the percentage of those who have taken a pregnancy test and are or have been pregnant: 30% of those who have taken a pregnancy test are or have been pregnant.
To find the percentage of women age 20 and under who are or have been pregnant, we multiply these probabilities: 50% x 30% = 15%. Therefore, 15% of women age 20 and under are or have been pregnant.
2) Given that a woman took a pregnancy test, we want to find the probability that she had a false negative test.
The probability of a false negative test is given as 13%. Since we are only considering women who took a pregnancy test, we can use this probability directly. Therefore, the probability that a woman had a false negative test is 13%.
3) For a woman who received a negative pregnancy test, we want to find the probability that she actually was pregnant.
To find this probability, we need to consider both false negative and true negative results. The probability of a false negative test is 13%, which means that 87% of negative tests are true negatives.
Therefore, the probability that a woman who received a negative pregnancy test was actually pregnant is 1 - 87% = 13%.
4) For a woman who received a positive pregnancy test, we want to find the probability that she was not pregnant.
To find this probability, we need to consider both true positive and false positive results. The probability of a false positive test is given as 5%, which means that 95% of positive tests are true positives.
Therefore, the probability that a woman who received a positive pregnancy test was not pregnant is 1 - 95% = 5%.