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A certain pregnancy test comes back positive for 95 percent [#permalink]
13 Aug 2020, 01:29
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 nonpregnant 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
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Re: A certain pregnancy test comes back positive for 95 percent [#permalink]
13 Aug 2020, 14:08
1
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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.



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Re: A certain pregnancy test comes back positive for 95 percent [#permalink]
13 Aug 2020, 14:50
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
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
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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
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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 nonpregnant. The test gives 5% false positives (as it is 95% accurate). So, no. of nonpregnant 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





