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Probability question..

E

Excelsior

Lifer
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?

 
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. 🙂
 
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 %
 
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 %
Click to expand...

That's not what the question asked
 
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?
Click to expand...

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.
 
Originally posted by: mugs
Originally posted by: Excelsior
Neither of those worked. Damnit.
Click to expand...

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

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.
 
Originally posted by: Excelsior
Originally posted by: mugs
Originally posted by: Excelsior
Neither of those worked. Damnit.
Click to expand...

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

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.
Click to expand...

Weird... Mug's should've been right.
 
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
 
Originally posted by: TuxDave
Originally posted by: Excelsior
Originally posted by: mugs
Originally posted by: Excelsior
Neither of those worked. Damnit.
Click to expand...

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

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.
Click to expand...

Weird... Mug's should've been right.
Click to expand...

I changed it at 11:59, before that I was dividing 6 by everything else instead of (6 * .98). I was off by .001 🙁
 
Dammit... it's late at night, I'm acting out of character. Let me try this again.

DO YOUR OWN HOMEWORK!! 😛
 
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!! 😛
Click to expand...

It wasn't my homework in the first place.
Click to expand...

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