Cancer probability

[Leafy]

(No, this isn't a homework problem. Just for the lulz of everyone who will get it wrong)

If 0.5% of the population have cancer, and there is a 98% accurate test (98% who have cancer test positive), and you receive a positive result, what is the probability of your having cancer? (at least 4 decimal places)

25 cents to whoever solves it first.

Phrased differently, What is the probability you have cancer given a positive test result?

 

[rudeguy]

42

 

[olds]

50/50
Either you have it or you don't.

 

[Colt45]

1

 

[olds]

Originally posted by: NSFW
20%

Fixed

 

[KLin]

Originally posted by: oldsmoboat
50/50
Either you have it or you don't.

I believe this to be the correct answer.

 

[Leafy]

Originally posted by: oldsmoboat

Originally posted by: NSFW
20%

Fixed

Get it to 4 places.

 

[Numenorean]

98.0000%

The accuracy of the test doesn't change so the .5% of people having cancer is irrelevant.

You told us that this test is 98%, so if you receive a positive result, then you have a 98% chance of being positive in this scenario.

 

[Colt45]

1.0000

 

[Leafy]

Originally posted by: Numenorean
98.0000%

The accuracy of the test doesn't change so the .5% of people having cancer is irrelevant.

You told us that this test is 98%, so if you receive a positive result, then you have a 98% chance of being positive in this scenario.

Fail. If the question was "What is the probability that you test positive given that you have cancer" instead of "What is the probability that you have cancer given that you test positive," you'd be right.

 

[Cattlegod]

100%

 

[mwmorph]

Originally posted by: Leafy
(No, this isn't a homework problem. Just for the lulz of everyone who will get it wrong)

If 0.5% of the population have cancer, and there is a 98% accurate test (98% who have cancer test positive), and you receive a positive result, what is the probability of your having cancer? (at least 4 decimal places)

25 cents to whoever solves it first.

You've been watching the Ted Talks haven't you?

 

[Leafy]

Originally posted by: mwmorph

Originally posted by: Leafy
(No, this isn't a homework problem. Just for the lulz of everyone who will get it wrong)

If 0.5% of the population have cancer, and there is a 98% accurate test (98% who have cancer test positive), and you receive a positive result, what is the probability of your having cancer? (at least 4 decimal places)

25 cents to whoever solves it first.

You've been watching the Ted Talks haven't you?

The what?

 

[biggestmuff]

Originally posted by: Cattlegod
100%

 

[Numenorean]

Originally posted by: Leafy

Originally posted by: Numenorean
98.0000%

The accuracy of the test doesn't change so the .5% of people having cancer is irrelevant.

You told us that this test is 98%, so if you receive a positive result, then you have a 98% chance of being positive in this scenario.

Fail. If the question was "What is the probability that you test positive given that you have cancer" instead of "What is the probability that you have cancer given that you test positive," you'd be right.

So now you are going to ask a different question than what you asked in the OP? Here's what you said in case you have brain cancer and can't remember what you just freaking typed or where the scroll wheel went to on your mouse:

If 0.5% of the population have cancer, and there is a 98% accurate test (98% who have cancer test positive), and you receive a positive result, what is the probability of your having cancer? (at least 4 decimal places)

25 cents to whoever solves it first.

Phrased differently, What is the probability you have cancer given a positive test result?"

 

[Leafy]

Originally posted by: Numenorean

Originally posted by: Leafy

Originally posted by: Numenorean
98.0000%

The accuracy of the test doesn't change so the .5% of people having cancer is irrelevant.

You told us that this test is 98%, so if you receive a positive result, then you have a 98% chance of being positive in this scenario.

Fail. If the question was "What is the probability that you test positive given that you have cancer" instead of "What is the probability that you have cancer given that you test positive," you'd be right.

So now you are going to ask a different question than what you asked in the OP? Here's what you said in case you have brain cancer and can't remember what you just freaking typed or where the scroll wheel went to on your mouse:

If 0.5% of the population have cancer, and there is a 98% accurate test (98% who have cancer test positive), and you receive a positive result, what is the probability of your having cancer? (at least 4 decimal places)

25 cents to whoever solves it first.

Phrased differently, What is the probability you have cancer given a positive test result?"

You're going to feel really dumb if I cancel it to prove it to you.

 

[FleshLight]

.98 * .005 = whatever

 

[Rufus12]

I forget probability stuff. Do I use normalcdf to solve this? I should know this. lol
BTW I'm pretty sure we need to know the % that have cancer when they test negative to solve this.

 

[Leafy]

Originally posted by: Rufus12
I forget probability stuff. Do I use normalcdf to solve this? I should know this. lol
BTW I'm pretty sure we need to know the % that have cancer when they test negative to solve this.

It's 2%, but you could have derived that from what I said.

 

[thecrecarc]

Ok, anyone agree the OP fails?

 

[Colt45]

massive fail.

 

[Leafy]

19.76%, and if oldsmoboat gives me his paypal I will donate the huge sum of $0.25 to him.

Given that 0.5% of the population has cancer, and the test is 98% accurate - 98% of people who have cancer test positive, and 98% of people who don't have cancer test negative:

Take a population of 10,000. 0.5% of the population has cancer, or 50 people.
9950 people thus don't have cancer.

Of the 50 that have cancer, 98% test positive (49 of the 50)
Of the 50 that have cancer, 2% test negative (1 of the 50)

Of the 9950 that don't have cancer, 2% test positive (199 of the 9950)
Of the 9950 that don't have cancer, 98% test negative (9751 of the 9950)

Total positive tests: (49 + 199) = 248
Total negative tests: (1 + 9751) = 9752

Of the 248 positive tests, 199 have cancer (2%) and 49 do.
49 actual cancers / 248 positive tests = 19.76%

 

[mugs]

Originally posted by: Colt45
1.0000

This. The problem didn't say anything about false positives.

 

[mugs]

Originally posted by: Leafy

Originally posted by: Rufus12
I forget probability stuff. Do I use normalcdf to solve this? I should know this. lol
BTW I'm pretty sure we need to know the % that have cancer when they test negative to solve this.

It's 2%, but you could have derived that from what I said.

No it's not.

 

[Numenorean]

Originally posted by: Leafy

Originally posted by: Numenorean

Originally posted by: Leafy

Originally posted by: Numenorean
98.0000%

The accuracy of the test doesn't change so the .5% of people having cancer is irrelevant.

You told us that this test is 98%, so if you receive a positive result, then you have a 98% chance of being positive in this scenario.

Fail. If the question was "What is the probability that you test positive given that you have cancer" instead of "What is the probability that you have cancer given that you test positive," you'd be right.

So now you are going to ask a different question than what you asked in the OP? Here's what you said in case you have brain cancer and can't remember what you just freaking typed or where the scroll wheel went to on your mouse:

If 0.5% of the population have cancer, and there is a 98% accurate test (98% who have cancer test positive), and you receive a positive result, what is the probability of your having cancer? (at least 4 decimal places)

25 cents to whoever solves it first.

Phrased differently, What is the probability you have cancer given a positive test result?"

You're going to feel really dumb if I cancel it to prove it to you.

Cancel what?

You're wrong. If you aren't wrong, then you don't know how to properly use the English language to write out a coherent request.

If you receive a positive result, then 98% of the time you will have cancer. Both ways you asked the question in the OP are asking that chance based on you receiving a positive test result. You didn't say anything about having cancer, not that it matters. If you have cancer and are given a positive test, it's still 98% - if you KNOW you have cancer then it's 100% because you already know and then the test won't matter. If you are given a false result and you KNOW you have cancer you still have a 100% chance of having cancer.

Now if you are going to ask a DIFFEFERENT question - i.e. If you KNOW you have cancer and are tested, what is the chance that the test result comes back positive? That's a completely different question. But it still has the same answer. 2% of the time, the test will fail. In this case, return a false negative (since you know you have cancer the negative is false) - so still you have a 98% chance of receiving a positive result, even though you already know you have it. Knowing you have it doesn't change the accuracy of the test.

OP = FAIL