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 and the given information. Let's work through each question step-by-step:
1) Assuming that none of the women who did not take a pregnancy test were pregnant, we need to find the percentage of women age 20 and under who are or have been pregnant. From the given data, we know that 50% of women age 20 and younger have taken a pregnancy test, and 30% of those who took the test are or have been pregnant.
To calculate the percentage of women who are or have been pregnant, we can multiply these two probabilities together:
Percentage of women who are or have been pregnant = 50% (women who took a pregnancy test) × 30% (women who are or have been pregnant among those who took a test)
Percentage of women who are or have been pregnant = (50/100) × (30/100) = 15/100 = 15%
Therefore, 15% of women age 20 and under are or have been pregnant.
2) Given that a woman took a pregnancy test, we need to find the probability that she had a false negative test. From the given data, we know that over-the-counter pregnancy tests give a false negative 13% of the time.
To calculate this probability, we use the probability of a false negative test among those who took the test:
Probability of a false negative = 13%
Therefore, the probability that a woman had a false negative test is 13%.
3) For a woman who received a negative pregnancy test, we need to find the probability that she actually was pregnant. From the given data, we know that over-the-counter pregnancy tests give a false positive 5% of the time.
To calculate this probability, we use the probability of a false positive test among those who took the test:
Probability of a false positive = 5%
Now, to find the probability that a woman who received a negative test was actually pregnant, we can subtract the false positive rate from 100%:
Probability of being pregnant with a negative test = 100% - Probability of a false positive
Probability of being pregnant with a negative test = 100% - 5% = 95%
Therefore, the probability that a woman who received a negative pregnancy test was actually pregnant is 95%.
4) For a woman who received a positive pregnancy test, we need to find the probability that she was not pregnant. From the given data, we know that over-the-counter pregnancy tests give a false positive 5% of the time.
To calculate this probability, we use the probability of a false positive test among those who took the test:
Probability of a false positive = 5%
Now, to find the probability that a woman who received a positive test was not actually pregnant, we can subtract the true positive rate from 100%:
Probability of not being pregnant with a positive test = 100% - Probability of being pregnant with a positive test
From question 1, we calculated that the percentage of women who are or have been pregnant is 15%. Therefore, the true positive rate is 15%.
Probability of not being pregnant with a positive test = 100% - 15% = 85%
Therefore, the probability that a woman who received a positive pregnancy test was not pregnant is 85%.
I hope this helps! Let me know if you have any further questions.
I have seen your repeated questions. Clearly, no one watching here feels confident in their ability to answer. I took a statistics class 50 years ago, and I'm sure if I pored over the matter again, I could figure it out, but that's too much trouble. Surely by this time you could have found similar exercises in your text, or online.
But I guess that's too much trouble for you, too.
I have tried looking at similar answers and I am not sure I am correct... and I am not a mind reader to know you don't feel confident....thanks anyway ..didn't mean for you to be too troubled
1).5*.3=.15=15%, multiply percent of <20 age women times percent that are pregnant
2)13%, from problem
3)False negative means the result is irrelevant. Therefore, percentage is 30%
4)70%, same reasoning as above