GATE2014 AG: GA-10

Question

$10$% of the population in a town is $\text{HIV}\large ^{+}$. A new diagnostic kit for $\text{HIV}$ detection is available; this kit correctly identifies $\text{HIV}\large ^{+}$ individuals $95$% of the time, and $\text{HIV}\large ^{-}$ individuals $89$% of the time. A particular patient is tested using this kit and is found to be positive. The probability that the individual is actually positive is ______.

Answer 1

If you dont like Bayes theorem then use this TREE METHOD:

Probability$=\dfrac{0.10\times 0.95}{0.10\times 0.95 + 0.90\times 0.11}$

$\hspace{1.9 cm} =0.4896$

Comments

ooh yes....HIV- i.e not infected all...LOL I was not able to understand that....

Thanks bro and sorry for such silly question..

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excellent approach  it is also applied pipeling coa questions

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This method is a game changer. Thanks for using it.

Answer 2

HIV⁺  10% of population

then HIV^- is 90% of population

the kit correctly identifies HIV⁺ in 95% of time

the kit incorrectly identifies HIV^- in (100-89)%= 11% of time

So, applying Baye's theorem 

        0.10⨉ 0.95                

.10⨉0.95 +  0.90⨉0.11

=0.4896

Comments

@srestha: can you please let me know where it is written in question that whole population in that town is infected.....
What I calculated is   

0.95 * o.1 / (o.95*0.1 + 0.05 + 0.9) = 0.68

considering only 10% population infected with HIV+ but don't know about other 90%... please correct me if I am going wrong..

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Probability= no. Of outcomes/ total no of outcomes

No. Of outcomes = 0.89

Total outcomes = 0.89 + 0.95= 1.84

So probability= 0.89/1.84

                         = 0.48 ans.

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@srestha ma'am

In GATE, upto how many decimal places should I keep the answer when nothing is mentioned explicitly? Is 2 places of decimal a safe bet?

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It will give( if they want approximate value), otherwise put exact answer

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@srestha In this question, nothing has been specified, so what should be done here?