Probability question..

[Excelsior]

In a rural area the fraction of the population that is HIV infected is 0.0006 (6 people per 10,000). The blood test for HIV infection returns a "positive" test result 98% of the time when the test is used on an infected person, and 1% of the time when used on an uninfected person. Evaluate the answer to as many decimal places as your calculator allows.

Question: If a person's test result comes back "positive", what is the probability he is actually HIV infected?

 

[Excelsior]

Bump.

 

[nycxandy]

I can do it, but not now.

If you still need it, I'll do it by 1AM.

 

[mugs]

Figure out how many positives there would be per 10,000 people, and divide (6*.98) by that number.

Edit: Text

(number of correct positive) / (number of total positives)
number of correct positives = 6*.98
number of total positives = number of correct positives (^) + number of false positives
number of false positives = .01 * 9994


About 5%. Makes sense, as the false positive rate is much higher than the acutal HIV infection rate.

But I've been known to be wrong in the past.

 

[her209]

Out of 10,000 people:

6 * 0.98 = 5.88 (correct)
9994 * 0.01 = 99.94 (incorrect)
9994 - 99.94 = 9894.06 (correct)

9894.06 + 5.88 = 9899.94 (correct)

9899.94 / 10000 = 0.989994 = 98.9994 %

 

[mugs]

Originally posted by: her209
Out of 10,000 people:

6 * 0.98 = 5.88 (correct)
9994 * 0.01 = 99.94 (incorrect)
9994 - 99.94 = 9894.06 (correct)

9894.06 + 5.88 = 9899.94 (correct)

9899.94 / 10000 = 0.989994 = 98.9994 %

That's not what the question asked

 

[chuckywang]

IM me at chuckywang and I'll help you.

 

[HonkeyDonk]

i'd be able to do this in a heart beat one year ago heh.

 

[Excelsior]

Neither of those worked. Damnit.

 

[mugs]

Originally posted by: Excelsior
Neither of those worked. Damnit.

I just changed my answer. Do you know what the actual answer is? How do you know we were wrong?

 

[TuxDave]

Originally posted by: Excelsior
In a rural area the fraction of the population that is HIV infected is 0.0006 (6 people per 10,000). The blood test for HIV infection returns a "positive" test result 98% of the time when the test is used on an infected person, and 1% of the time when used on an uninfected person. Evaluate the answer to as many decimal places as your calculator allows.

Question: If a person's test result comes back "positive", what is the probability he is actually HIV infected?

A = Hiv Positive
B = Test Positive

Use need to find p(A given B)

You are given p(B given A) so use the formula

p(A given B) = p(B given A)*p(A)/p(B)

p(B) = p(B & A) + p(B & !A)

p(A & B) = p(A)*p(B given A)
p(!A & B) = p(!A)*p(B given !A)

I hope I got that right.

 

[Excelsior]

Originally posted by: mugs

Originally posted by: Excelsior
Neither of those worked. Damnit.

I just changed my answer. Do you know what the actual answer is? How do you know we were wrong?

I was submitting your answers to a friends webassign (she never got it, the deadline was 12, and she submitted around 16 different answers, none of them worked, including yours). It's cool though.

 

[TuxDave]

Originally posted by: Excelsior

Originally posted by: mugs

Originally posted by: Excelsior
Neither of those worked. Damnit.

I just changed my answer. Do you know what the actual answer is? How do you know we were wrong?

I was submitting your answers to a friends webassign (she never got it, the deadline was 12, and she submitted around 16 different answers, none of them worked, including yours). It's cool though.

Weird... Mug's should've been right.

 

[MrX82]

P(infected)=0.0006
P("+"|+)=0.98
P("+"|-)=0.01

so you want
P(infected|"+")=P(infected, "+")/P("+")
=(P("+"|infected)*P(infected))/(P("+"|infected)*P(infected)+P("+"| not infected)*P(not infected))

hope this helps...


"+" means test reports positive
+ is actual state
- is actual state

 

[mugs]

Originally posted by: TuxDave

Originally posted by: Excelsior

Originally posted by: mugs

Originally posted by: Excelsior
Neither of those worked. Damnit.

I just changed my answer. Do you know what the actual answer is? How do you know we were wrong?

I was submitting your answers to a friends webassign (she never got it, the deadline was 12, and she submitted around 16 different answers, none of them worked, including yours). It's cool though.

Weird... Mug's should've been right.

I changed it at 11:59, before that I was dividing 6 by everything else instead of (6 * .98). I was off by .001

 

[TuxDave]

Dammit... it's late at night, I'm acting out of character. Let me try this again.

DO YOUR OWN HOMEWORK!!

 

[HomeBrewerDude]

baysian was what i was thinking but i don't remember the details.

 

[Excelsior]

Originally posted by: TuxDave
Dammit... it's late at night, I'm acting out of character. Let me try this again.

DO YOUR OWN HOMEWORK!!

It wasn't my homework in the first place.

 

[TuxDave]

Originally posted by: Excelsior

Originally posted by: TuxDave
Dammit... it's late at night, I'm acting out of character. Let me try this again.

DO YOUR OWN HOMEWORK!!

It wasn't my homework in the first place.

Oh.. ok, then just pass my message to your friend.