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## Where do I start?

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• Here is the problem A medical device applied to a person known to have a disease has a 95% probability of correctly indicating that the person has the disease.
Message 1 of 4 , Mar 2, 2005
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Here is the problem

A medical device applied to a person known to have a disease has a
95% probability of correctly indicating that the person has the
disease.

When applied to a person known to NOT have the disease, the device
has a 97% probability of correctly indicating that the person does
not have the disease.

I use the device and the result indicates I have the disease. 1 in
2000 actually have this disease.

What is the probability that I actually have the disease?

-comments, i was thinking that the probability is always 1 in 2000,
since the test is no 100% accurate, but I am probably wrong, any
suggestions would be great.
• Think of it this way - the device indicates you have the disease. This can happen only in two different ways: (a) You have the disease, and the device is
Message 2 of 4 , Mar 3, 2005
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Think of it this way - the device indicates you have the disease. This
can happen only in two different ways:

(a) You have the disease, and the device is correct
(b) You do not have the disease, and the device is wrong

(a) can happen with probability 1/2000 * 95 % = 0.0475 %
(b) can happen with probability 1999/2000 * 3% = 2.9985%

So the overall chance that a random person tests positive for the disease
is
0.0475% + 2.9985% = 3.046%

Given that you tested positive, the probability of (a) being the case, is
then
0.0475 % / 3.046% = 1.559% - Quite a low chance of having the disease!

Check http://www.acad.sunytccc.edu/instruct/sbrown/stat/falsepos.htm for a
simple illustration.

with regards,
Rino.

deltachamp1 <only4amillion@...>
03/03/05 03:31 AM
probability@yahoogroups.com

To
probability@yahoogroups.com
cc

Subject
[probability] Where do I start?

Here is the problem

A medical device applied to a person known to have a disease has a
95% probability of correctly indicating that the person has the
disease.

When applied to a person known to NOT have the disease, the device
has a 97% probability of correctly indicating that the person does
not have the disease.

I use the device and the result indicates I have the disease. 1 in
2000 actually have this disease.

What is the probability that I actually have the disease?

-comments, i was thinking that the probability is always 1 in 2000,
since the test is no 100% accurate, but I am probably wrong, any
suggestions would be great.

To visit your group on the web, go to:
http://groups.yahoo.com/group/probability/

To unsubscribe from this group, send an email to:
probability-unsubscribe@yahoogroups.com

[Non-text portions of this message have been removed]
• deltachamp1 wrote: Here is the problem A medical device applied to a person known to have a disease has a 95% probability of correctly
Message 3 of 4 , Mar 3, 2005
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deltachamp1 <only4amillion@...> wrote:

Here is the problem

A medical device applied to a person known to have a disease has a
95% probability of correctly indicating that the person has the
disease.

When applied to a person known to NOT have the disease, the device
has a 97% probability of correctly indicating that the person does
not have the disease.

I use the device and the result indicates I have the disease. 1 in
2000 actually have this disease.

What is the probability that I actually have the disease?

-comments, i was thinking that the probability is always 1 in 2000,
since the test is no 100% accurate, but I am probably wrong, any
suggestions would be great.

try to use Bayes theorem...or unconditional probability..i`m busy for my exam..i`ll atry to answer it later...u can ask at www.mathnerds.com

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• Hi, you can solve the problem by using Bayes theorem. But you don t need to know the theorem to solve the problem. It helps to think in terms of absolute
Message 4 of 4 , Mar 5, 2005
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Hi,

you can solve the problem by using Bayes' theorem. But you don't need to
know the theorem to solve the problem.

It helps to think in terms of absolute numbers instead of probability, this
is easier for our brains.

Image 1000000 people. 1 in 2000 have the disease, so 500 have it and 999500
don't have it.
The medical test will discover 95% of the diseased people: 475 will be
diagnosed as ill.

Alas, the test will also incorrectly state that 3% of the healthy persons
have the disease: 29985 people will receive this bad news.

So in total, 30460 persons are diagnosed to be ill. Only 475 of them really
are. The probability of really being ill when diagnosed as ill is therefore
475/30460 = 0.01559. This is rather good news, isn't it? When the test tells
you you're ill, you probably aren't! That explains why one usually has to
undergo 'further tests' before the doctor will make any statement.

When you divide all absolute numbers by 1000000, you have applied Bayes'
law.

Pedro

-----Original Message-----
Sent: Friday, March 04, 2005 6:13 AM
To: probability@yahoogroups.com
Subject: Re: [probability] Where do I start?

deltachamp1 <only4amillion@...> wrote:

Here is the problem

A medical device applied to a person known to have a disease has a
95% probability of correctly indicating that the person has the
disease.

When applied to a person known to NOT have the disease, the device
has a 97% probability of correctly indicating that the person does
not have the disease.

I use the device and the result indicates I have the disease. 1 in
2000 actually have this disease.

What is the probability that I actually have the disease?

-comments, i was thinking that the probability is always 1 in 2000,
since the test is no 100% accurate, but I am probably wrong, any
suggestions would be great.

try to use Bayes theorem...or unconditional probability..i`m busy for my
exam..i`ll atry to answer it later...u can ask at www.mathnerds.com

---------------------------------

To visit your group on the web, go to:
http://groups.yahoo.com/group/probability/

To unsubscribe from this group, send an email to:
probability-unsubscribe@yahoogroups.com

---------------------------------
Celebrate Yahoo!'s 10th Birthday!
Yahoo! Netrospective: 100 Moments of the Web

[Non-text portions of this message have been removed]

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