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A terrible disease sweeps around the world, luckily only affecting 1

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Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132595 [1], given: 12326

A terrible disease sweeps around the world, luckily only affecting 1 [#permalink]

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06 Oct 2017, 01:49
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Difficulty:

85% (hard)

Question Stats:

10% (02:05) correct 90% (00:54) wrong based on 38 sessions

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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. $$\frac{99}{100}$$
[Reveal] Spoiler: OA

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Kudos [?]: 132595 [1], given: 12326

Manager
Joined: 30 Mar 2017
Posts: 69

Kudos [?]: 18 [0], given: 11

Re: A terrible disease sweeps around the world, luckily only affecting 1 [#permalink]

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06 Oct 2017, 02:03
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.

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Kudos [?]: 18 [0], given: 11

Intern
Joined: 20 Sep 2017
Posts: 1

Kudos [?]: 0 [0], given: 4

Re: A terrible disease sweeps around the world, luckily only affecting 1 [#permalink]

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06 Oct 2017, 03:55
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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Intern
Joined: 02 Feb 2016
Posts: 19

Kudos [?]: 4 [0], given: 54

Re: A terrible disease sweeps around the world, luckily only affecting 1 [#permalink]

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06 Oct 2017, 16:41
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.

Kudos [?]: 4 [0], given: 54

Director
Joined: 18 Aug 2016
Posts: 550

Kudos [?]: 161 [0], given: 134

GMAT 1: 630 Q47 V29
Re: A terrible disease sweeps around the world, luckily only affecting 1 [#permalink]

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07 Oct 2017, 01:51
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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Thanks
Luckisnoexcuse

Kudos [?]: 161 [0], given: 134

Math Expert
Joined: 02 Aug 2009
Posts: 5201

Kudos [?]: 5826 [2], given: 117

Re: A terrible disease sweeps around the world, luckily only affecting 1 [#permalink]

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07 Oct 2017, 05:27
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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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Kudos [?]: 5826 [2], given: 117

Re: A terrible disease sweeps around the world, luckily only affecting 1   [#permalink] 07 Oct 2017, 05:27
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