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A certain pregnancy test comes back positive for 95 percent
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13 Aug 2020, 01:29
13 Aug 2020, 01:29
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Question Stats:
52% (02:15) correct
47% (01:59) wrong based on 123 sessions
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A certain pregnancy test comes back positive for 95 percent of pregnant women who take it. However, it also comes back positive for 5 percent of non-pregnant women who take it. Two percent of the female population of city A is pregnant. Marisa, a resident of city A, takes the pregnancy test and gets a positive result.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
KUDOS for the right solution and explanation
Quantity A |
Quantity B |
The probability that Marisa is pregnant |
75 % |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
KUDOS for the right solution and explanation
A certain pregnancy test comes back positive for 95 percent
[#permalink]
14 Feb 2022, 04:30
14 Feb 2022, 04:30
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For the sake of clarity, I've amended the last sentence of the prompt and the wording for Quantity A:
This is an EITHER-OR problem.
Every female resident is EITHER pregnant OR not.
The test result for every female resident is EITHER positive OR negative.
For an either-or problem, use a MATRIX to organize the data, as shown below:
Screen Shot 2022-02-14 at 7.00.32 AM.png [ 61.52 KiB | Viewed 3217 times ]
Two percent of the female population of city A is pregnant.
Let the total number of women = 10,000.
Since 2% of these 10,000 women are pregnant, the following matrix is yielded:
Screen Shot 2022-02-14 at 7.04.01 AM.png [ 65.4 KiB | Viewed 3184 times ]
A certain pregnancy test comes back positive for 95 percent of pregnant women who take it.
However, it also comes back positive for 5 percent of non-pregnant women who take it.
In the preceding matrix:
A negative result is yielded for 5% of the 200 pregnant women = 10 women
A positive result is yielded for 5% of the 9,800 non-pregnant women = 490 women
The following matrix is yielded:
Screen Shot 2022-02-14 at 7.11.20 AM.png [ 72.83 KiB | Viewed 3205 times ]
In the resulting matrix, 190 of the 680 positive results are yielded by pregnant women.
Thus:
The probability that Marissa's positive result indicates an actual pregnancy = 190/680 = much less than 75%.
Quantity B is larger.
Carcass wrote:
A certain pregnancy test comes back positive for 95 percent of pregnant women who take it. However, it also comes back positive for 5 percent of non-pregnant women who take it. Two percent of the female population of city A is pregnant. Yesterday, every woman who resides in city A took the test, and Marisa, a female resident of city A, got a positive result.
Quantity A |
Quantity B |
The probability that Marisa's test indicated an actual pregnancy |
75 % |
This is an EITHER-OR problem.
Every female resident is EITHER pregnant OR not.
The test result for every female resident is EITHER positive OR negative.
For an either-or problem, use a MATRIX to organize the data, as shown below:
Attachment:
Screen Shot 2022-02-14 at 7.00.32 AM.png [ 61.52 KiB | Viewed 3217 times ]
Two percent of the female population of city A is pregnant.
Let the total number of women = 10,000.
Since 2% of these 10,000 women are pregnant, the following matrix is yielded:
Attachment:
Screen Shot 2022-02-14 at 7.04.01 AM.png [ 65.4 KiB | Viewed 3184 times ]
A certain pregnancy test comes back positive for 95 percent of pregnant women who take it.
However, it also comes back positive for 5 percent of non-pregnant women who take it.
In the preceding matrix:
A negative result is yielded for 5% of the 200 pregnant women = 10 women
A positive result is yielded for 5% of the 9,800 non-pregnant women = 490 women
The following matrix is yielded:
Attachment:
Screen Shot 2022-02-14 at 7.11.20 AM.png [ 72.83 KiB | Viewed 3205 times ]
In the resulting matrix, 190 of the 680 positive results are yielded by pregnant women.
Thus:
The probability that Marissa's positive result indicates an actual pregnancy = 190/680 = much less than 75%.
Quantity B is larger.
Show: ::
B
General Discussion
Re: A certain pregnancy test comes back positive for 95 percent
[#permalink]
13 Aug 2020, 14:08
13 Aug 2020, 14:08
4
Event + = positive result
Event - = negative result
Event P= woman is pregnant
Event NP= woman is not pregnant
Given:
We are told that given you are pregnant the test results positive 95% of the time. Therefore
Pr(+|P)=.95
We are told that given you are not pregnant the test results positive 5% of the time. Therefore
Pr(+|NP)=.05
We are told 2% of the population is pregnant Therefore
Pr(P)=.02
Pr(NP)=.98
We are looking for: Given that Marissa tested positive what is the probability she is pregnant?
That is, we are looking for: Pr(P|+)
Pr(P|+)
=Pr(P,+)/Pr(+)
Notice
Pr(+|P)=Pr(P,+)/Pr(P)
Therefore Pr(p,+)=Pr(P)Pr(+|P)
Also
Pr(+|NP)=Pr(NP,+)/Pr(NP)
Therefore Pr(NP,+)=Pr(NP)Pr(+|NP)
Also
Pr(+)=Pr(P,+)+Pr(NP,+)=Pr(P)Pr(+|P)+Pr(NP)Pr(+|NP)
So we get
Pr(P|+)
=Pr(P,+)/Pr(+)
=Pr(P)Pr(+|P)/ [Pr(P)Pr(+|P)+Pr(NP)Pr(+|NP)]
=(.02)(.95)/ [(.02)*(.95) + (.98)(.05)]
= .019/(.019+ .049)
= .279
.279<.75
Final Answer: B
PS: This is definitely not on the GRE. This question required Bayes Theorem and Law of Total Probability, both of which are out of scope for the GRE.
Event - = negative result
Event P= woman is pregnant
Event NP= woman is not pregnant
Given:
We are told that given you are pregnant the test results positive 95% of the time. Therefore
Pr(+|P)=.95
We are told that given you are not pregnant the test results positive 5% of the time. Therefore
Pr(+|NP)=.05
We are told 2% of the population is pregnant Therefore
Pr(P)=.02
Pr(NP)=.98
We are looking for: Given that Marissa tested positive what is the probability she is pregnant?
That is, we are looking for: Pr(P|+)
Pr(P|+)
=Pr(P,+)/Pr(+)
Notice
Pr(+|P)=Pr(P,+)/Pr(P)
Therefore Pr(p,+)=Pr(P)Pr(+|P)
Also
Pr(+|NP)=Pr(NP,+)/Pr(NP)
Therefore Pr(NP,+)=Pr(NP)Pr(+|NP)
Also
Pr(+)=Pr(P,+)+Pr(NP,+)=Pr(P)Pr(+|P)+Pr(NP)Pr(+|NP)
So we get
Pr(P|+)
=Pr(P,+)/Pr(+)
=Pr(P)Pr(+|P)/ [Pr(P)Pr(+|P)+Pr(NP)Pr(+|NP)]
=(.02)(.95)/ [(.02)*(.95) + (.98)(.05)]
= .019/(.019+ .049)
= .279
.279<.75
Final Answer: B
PS: This is definitely not on the GRE. This question required Bayes Theorem and Law of Total Probability, both of which are out of scope for the GRE.
