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A terrible disease sweeps around the world, luckily only affecting 1 [#permalink]
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06 Oct 2017, 00:49
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CHALLENGE QUESTIONS A terrible disease sweeps around the world, luckily only affecting 1 in 10,000, but for that one, the disease is lethal. Shortly after the disease was discovered, scientists developed a test that is 99% accurate regardless of whether you have the disease. In other words, the test yields the correct positive or correct negative result 99% of the time. You take the test and a week later, you receive the lab report. The outcome of the test is positive. What is the probability you have the disease? A. \(\frac{99}{1,000,000}\) B. \(\frac{1}{102}\) C. \(\frac{1}{100}\) D. \(\frac{10,099}{1,000,000}\) E. \(\frac{99}{100}\)
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Re: A terrible disease sweeps around the world, luckily only affecting 1 [#permalink]
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06 Oct 2017, 01:03
The answer should be E. As there is no connection with 1 in 10000, and there are still 99% chances of him having the disease. So the probability will be 99/100. Sent from my Moto G (5) Plus using GMAT Club Forum mobile app



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Re: A terrible disease sweeps around the world, luckily only affecting 1 [#permalink]
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06 Oct 2017, 02:55
Probability of having the disease * probability of test accuracy = (1/10000) * (99/100) = 99/1,000,000 A is the correct ans



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Re: A terrible disease sweeps around the world, luckily only affecting 1 [#permalink]
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06 Oct 2017, 15:41
The question indicates that only 1 person took the test, so the results are only related to this sample size. The 1/10000 probability of having disease seems like extra information(?). I think the answer is 99/100.



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Re: A terrible disease sweeps around the world, luckily only affecting 1 [#permalink]
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07 Oct 2017, 00:51
Bunuel wrote: CHALLENGE QUESTIONS A terrible disease sweeps around the world, luckily only affecting 1 in 10,000, but for that one, the disease is lethal. Shortly after the disease was discovered, scientists developed a test that is 99% accurate regardless of whether you have the disease. In other words, the test yields the correct positive or correct negative result 99% of the time. You take the test and a week later, you receive the lab report. The outcome of the test is positive. What is the probability you have the disease? A. \(\frac{99}{1,000,000}\) B. \(\frac{1}{102}\) C. \(\frac{1}{100}\) D. \(\frac{10,099}{1,000,000}\) E. \(\frac{99}{100}\) out of 10000 people 1 has the disease if 10000 people are tested, 1% of people will lie in grey area i.e. wrong test result (test showing positive but negative or test showing negative but positive) 1/100
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Re: A terrible disease sweeps around the world, luckily only affecting 1 [#permalink]
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07 Oct 2017, 04:27
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Bunuel wrote: CHALLENGE QUESTIONS A terrible disease sweeps around the world, luckily only affecting 1 in 10,000, but for that one, the disease is lethal. Shortly after the disease was discovered, scientists developed a test that is 99% accurate regardless of whether you have the disease. In other words, the test yields the correct positive or correct negative result 99% of the time. You take the test and a week later, you receive the lab report. The outcome of the test is positive. What is the probability you have the disease? A. \(\frac{99}{1,000,000}\) B. \(\frac{1}{102}\) C. \(\frac{1}{100}\) D. \(\frac{10,099}{1,000,000}\) E. \(\frac{99}{100}\)* Hi... It is a tough Q if you don't understand the wordings and is ofcourse TRICKY and that is why none have got the correct answer above. The result is POSITIVE.. Two cases.. 1) Correct: 99% So he is 1 out of 10000. Probability= \(\frac{1}{10000}*\frac{99}{100}=\frac{99}{1000000}\).. 2) Wrong: 1% So he is out of 9999.. Probability= \(\frac{9999}{10000}*\frac{1}{100}=\frac{9999}{1000000}\).. So PROBABILITY that it is correct = (99/1000000)/(99/1000000+9999/1000000) =\(\frac{99}{99(1+101)}=1/102\) B
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A terrible disease sweeps around the world, luckily only affecting 1 [#permalink]
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06 Dec 2017, 23:39
Great question on conditional probability.
P(A happening / given B occured) = P(A AND B)/P(B)
P(You have disease/given outcome is positive) = P(you have disease AND outcome is positive)/P(outcome is positive)
P(outcome is positive) = false positive + true positive = \((9999/10000)\) * \((1/100)\) + \((1/10000)\) * \((99/100)\)
P(you have disease AND outcome is positive) = \((1/10000) * (99/100)\)
So P(A given B) = P(You have disease/given outcome is positive) = \((1/10000) * (99/100)\) / (\((9999/10000)\) * \((1/100)\) + \((1/10000)\) * \((99/100)\))
= \(99 / (9999 + 99)\) = 1/ (1 + \(9999/99\)) = 1 / (1 + 101) = 1/ 102
Answer (B)




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