Another logical exercise

[En_Route]

Another hoary old chestnut but fun maybe for those to whom it is novel:

A test of a disease presents 5% false positives. The disease strikes 1/1000 of the population. People are tested at random without any evidence of predisposition or prior symptoms. A patient's test is positive. What is the chance he/she has the disease?

[Tank]

Another hoary old chestnut but fun maybe for those to whom it is novel:

A test of a disease presents 5% false positives. The disease strikes 1/1000 of the population. People are tested at random without any evidence of predisposition or prior symptoms. A patient's test is positive. What is the chance he/she has the disease?

95%. The prevalence of the disease in the population is irrelevant as this is post test.

If one were to take the same figures but say how many false positive per million of the population one would expect 1,000 cases but you'll have 1,050 as there are 5% false positives in the test to you'll get the 1,000 + 0.05*1000

[Ali]

Another hoary old chestnut but fun maybe for those to whom it is novel:

A test of a disease presents 5% false positives. The disease strikes 1/1000 of the population. People are tested at random without any evidence of predisposition or prior symptoms. A patient's test is positive. What is the chance he/she has the disease?

95%?

ETA:  ooooh, Tank thought the same thing I did, so it MUST be right.  Who's logical?  Who's logical?  A-li, A-li, A-li!!!! 

[En_Route]

Another hoary old chestnut but fun maybe for those to whom it is novel:

A test of a disease presents 5% false positives. The disease strikes 1/1000 of the population. People are tested at random without any evidence of predisposition or prior symptoms. A patient's test is positive. What is the chance he/she has the disease?

95%?

ETA:  ooooh, Tank thought the same thing I did, so it MUST be right.  Who's logical?  Who's logical?  A-li, A-li, A-li!!!! 

Don't count your non-infected chickens just yet my dear.

[Stevil]

Another hoary old chestnut but fun maybe for those to whom it is novel:

A test of a disease presents 5% false positives. The disease strikes 1/1000 of the population. People are tested at random without any evidence of predisposition or prior symptoms. A patient's test is positive. What is the chance he/she has the disease?

"5% false positives"
5% of what?
a) 5% of all the positive results
b) 5% of all the people tested?

if b then 5% of 1000 people = 50 people however only 1 will have he disease
1 is 2% of 50
so a positive result gives a person a 2% chance of having the disease.

[Asmodean]

Trick question. The chances are 1/1000 as that is the rate provided for actually having the disease independent of testing.

Minor edit: Stevil's way makes sense too, really, depending on what the question is actually aimed at.

[En_Route]

Another hoary old chestnut but fun maybe for those to whom it is novel:

A test of a disease presents 5% false positives. The disease strikes 1/1000 of the population. People are tested at random without any evidence of predisposition or prior symptoms. A patient's test is positive. What is the chance he/she has the disease?

"5% false positives"
5% of what?
a) 5% of all the positive results
b) 5% of all the people tested?

if b then 5% of 1000 people = 50 people however only 1 will have he disease
1 is 2% of 50
so a positive result gives a person a 2% chance of having the disease.

False positive rates are always expressed by reference to the number of tests. So 2% it is. What is interesting  in an alarming but not very surprising way is that a lot of doctors got the answer wrong.

[Ali]

Another hoary old chestnut but fun maybe for those to whom it is novel:

A test of a disease presents 5% false positives. The disease strikes 1/1000 of the population. People are tested at random without any evidence of predisposition or prior symptoms. A patient's test is positive. What is the chance he/she has the disease?

"5% false positives"
5% of what?
a) 5% of all the positive results
b) 5% of all the people tested?

if b then 5% of 1000 people = 50 people however only 1 will have he disease
1 is 2% of 50
so a positive result gives a person a 2% chance of having the disease.

*Cocks head to the side like a spaniel.  Thinks a long time.  Re-reads explanation 3x*  Nope, still don't understand why it's 5% of 1000 and only one will have the disease.  *Shakes head.  Goes back to playing Draw Something*

[DeterminedJuliet]

I think I get this one! Do I get a cookie? 

[OldGit]

^ Your choice.  1 in 50 cookies contain strong laxatives and there are 31 cookies on the plate.  All cookies were baked by a man with long hair.

[Asmodean]

...So there is a one in one chance of there being hair in it.

[DeterminedJuliet]

  This reward does not feel very rewarding all of a sudden...
How's the man's hygiene?

[En_Route]

This reward does not feel very rewarding all of a sudden...
How's the man's hygiene?

He has a bath every month even if he doesn't need it.

[Asmodean]

Also, some dreads which he packs in a plastic bag before bathing, yes? 

[DeterminedJuliet]

Errmmm. I may just purchase some cookies.