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A certain pregnancy test comes back positive for 95 percent

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A certain pregnancy test comes back positive for 95 percent [#permalink]  13 Aug 2020, 01:29
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Question Stats:

52% (02:15) correct 47% (01:58) wrong based on 44 sessions
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.

 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
[Reveal] Spoiler: OA

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Re: A certain pregnancy test comes back positive for 95 percent [#permalink]  13 Aug 2020, 14:08
1
KUDOS
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

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.
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Re: A certain pregnancy test comes back positive for 95 percent [#permalink]  13 Aug 2020, 14:50
Expert's post
Kudos to you Sir for solving it, though

Kaplan way
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Re: A certain pregnancy test comes back positive for 95 percent [#permalink]  10 Sep 2020, 11:59
Does it matter if none of the pregnant women of the town have taken the test? That was not stated
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Re: A certain pregnancy test comes back positive for 95 percent [#permalink]  10 Sep 2020, 13:04
Expert's post
I think the question asks you a different thing
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Re: A certain pregnancy test comes back positive for 95 percent [#permalink]  13 Sep 2020, 04:58
I think it does too, but I also know that the GRE cannot leave wiggle room. But I was genuinely asking rather than just pointing out a possible loophole... if in fact none of the women had taken that pregnancy test but were pregnant, how would that affect the % confidence? In other words, assume none of them took it; assume half had taken it; how would that change the answer? could it even be answered?
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Re: A certain pregnancy test comes back positive for 95 percent [#permalink]  13 Sep 2020, 08:36
1
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Expert's post
rydercourtney1 wrote:
I think it does too, but I also know that the GRE cannot leave wiggle room. But I was genuinely asking rather than just pointing out a possible loophole... if in fact none of the women had taken that pregnancy test but were pregnant, how would that affect the % confidence? In other words, assume none of them took it; assume half had taken it; how would that change the answer? could it even be answered?

Don't spend anymore time on the question.
As @chacinluis noted, this question is way beyond the scope of the GRE.
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Re: A certain pregnancy test comes back positive for 95 percent [#permalink]  18 Oct 2020, 10:34
1
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Let's say there are 1000 women in town.
2% are pregnant. So pregnant women = .02*1000 = 20
No. of pregnant women as indicated by the test = .95*20 = 19
980 are non-pregnant.
The test gives 5% false positives (as it is 95% accurate). So, no. of non-pregnant women who are shown pregnant by the test = .05*980 = 49
Total no. of pregnant women as indicated by the test = 49+19 = 68
So, the probability that a random woman who takes the test (Marisa in this question) is pregnant = 19/68 ~28%, which is less than 75%.
Hence, the final answer is B.
Re: A certain pregnancy test comes back positive for 95 percent   [#permalink] 18 Oct 2020, 10:34
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