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

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

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New post 06 Oct 2017, 01:49
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A
B
C
D
E

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  95% (hard)

Question Stats:

8% (01:58) correct 92% (01:53) wrong based on 161 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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New post 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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Re: A terrible disease sweeps around the world, luckily only affecting 1  [#permalink]

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New post 06 Oct 2017, 02:03
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.

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

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

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New post 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

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

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New post 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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New post 06 Jul 2018, 11:49
BeingHan wrote:
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.

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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).
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Re: A terrible disease sweeps around the world, luckily only affecting 1 &nbs [#permalink] 06 Jul 2018, 11:49
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