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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: 60468
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:

95% (hard)

Question Stats:

10% (02:15) correct 90% (02:01) wrong based on 190 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. $$\frac{99}{100}$$

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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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7
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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07 Dec 2017, 00:39
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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

##### General Discussion
Manager
Joined: 30 Mar 2017
Posts: 67
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.

Sent from my Moto G (5) Plus using GMAT Club Forum mobile app
Intern
Joined: 20 Sep 2017
Posts: 1
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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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.
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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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Re: A terrible disease sweeps around the world, luckily only affecting 1  [#permalink]

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26 Jun 2018, 17:44
It should be E. 1 in 10000 not connected with taking test and still 99% chances are there for having the disease. So the probability is 99/100.
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Re: A terrible disease sweeps around the world, luckily only affecting 1  [#permalink]

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06 Jul 2018, 11:49
BeingHan wrote:
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

No. After being declared that he has disease, there are two possible cases.
1) He is among 1 of 10,000 and test result is correct (99 percent case)
2) He is among 99,99 people who dont have disease and test result is negative (1 percent case).
Re: A terrible disease sweeps around the world, luckily only affecting 1   [#permalink] 06 Jul 2018, 11:49
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