SOLUTION: A home pregnancy test was given to women, then pregnancy was verified through blood tests. The following table shows the home pregnancy test results. Positive Negative Total

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Question 1210435: A home pregnancy test was given to women, then pregnancy was verified through blood tests. The following table shows the home pregnancy test results.
Positive Negative Total
Pregnant 63 5 68
Not Pregnant 6 61 67
Total 69 66 135
Round your answers to the nearest thousandth.
P (positive pregnant) =
P (pregnant positive) =
P (negative pregnant) =
P(not pregnant negative) =
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(53765)   (Show Source): You can put this solution on YOUR website!
.
A home pregnancy test was given to women, then pregnancy was verified through blood tests. The following table shows the home pregnancy test results.
Positive Negative Total
Pregnant 63 5 68
Not Pregnant 6 61 67
Total 69 66 135
Round your answers to the nearest thousandth.
P (positive pregnant) =
P (pregnant positive) =
P (negative pregnant) =
P(not pregnant negative) =
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Dear writer,

I'd like to make couple of comments, regarding this post.


First, one sentence is missed in the post, which is a key in describing this probabilistic experiment.

This sentence says "One women was randomly selected from the group. Find the probability that "


Next, first and second questions are identical: you ask twice the same thing.

I do not think that this is done intently: I suspect it is a mistake, which should be fixed.


Also, notice that your post says "Round your answers to the nearest thousandth"
but it does not contain a question.

It is a bad style to compose Math problems this way.


Be aware.



Answer by Edwin McCravy(20081)   (Show Source): You can put this solution on YOUR website!
If you copy and paste your problem in Google, you get this solution by AI:

P(positive and pregnant) = 0.467
P(pregnant | positive) = 0.913
P(negative and pregnant) = 0.037
P(not pregnant|negative) = 0.924

Step 1: Identify the joint probabilities
The problem asks for four different probabilities based on the provided table.
First, we need to calculate the joint probability of a positive test and a
pregnancy, which is denoted as 

P(positive and pregnant) = 63/135 = 0.46666... approximately

The numerator is the number of women who are both pregnant and had a positive
test, which is 63. The denominator is the total number of women, 135.

P(positive and pregnant) = 63/135 = 0.46666... approximately

Rounding to the nearest thousandth gives 0.467

Next, we calculate the joint probability of a negative test and a pregnancy,
 
P(negative and pregnant) 

The numerator is the number of women who are pregnant and had a negative test,
which is 5. The denominator is the total number of women, 135.

P(negative and pregnant) = 5/135 = 0.03703... approximately

Rounding to the nearest thousandth gives: 0.037

Step 2: Identify and calculate the conditional probabilities
The remaining two probabilities are conditional probabilities, which are
calculated based on a subset of the total population.

P(pregnant|positive) = 63/69 = 0.91304... approximately
Rounding to the nearest thousandth gives 0.913.

P(not pregnant|negative) is the probability of a woman being pregnant given
that she had a positive test. The denominator is the total number of women with
a positive test, which is 69. The numerator is the number of women who are both
pregnant and had a positive test, which is 63.

P(pregnant|positive) = 63/69 = 0.91304... approximately

Rounding to the nearest thousandth gives 0.913

P(pregnant|negative) is the probability of a woman not being pregnant given that
she had a negative test. The denominator is the total number of women with a
negative test, which is 66. The numerator is the number of women who are both
not pregnant and had a negative test, which is 61.

P(not pregnant|negative) = 61/66 = 0.92424... approximately.

Rounding to the nearest thousandth gives 0.924

Google it yourself and see if I missed anything that the AI gave.

Edwin
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