probability

[furqan123]

Ali shows symptoms of Malaria and advised by the doctor to get tested for confirmation. The prescribed test method comes positive 85% of the time the patient
actually has Malaria. The test method gives false positive 10% of the time, i.e when the patient does not have Malaria. If 1.5% of the population is affected
by Malaria, what is the probability that Ali has been infected by Malaria provided he tested positive?

 

[Steven G]

What exactly do you need help with from this math help forum? Please post back showing us what you have done and where you need help. That way we will be able to give you expert help. Thanks.

 

[tkhunny]

#1 This is not a good question. Ali already shows symptoms. The search for a related prevalence via screening in the general population has little to do with Ali's condition.

He has it...
Test: 85% Correct, 15% Incorrect

Or he doesn't...
Test: 90% Correct, 10% Incorrect.

 

[pka]

\(\mathcal{P}(M|+)=\dfrac{\mathcal{P}(+|M)\mathcal{P}(M)}{\mathcal{P}(+|M)\mathcal{P}(M)+\mathcal{P}(+|\neg M)\mathcal{P}(\neg M)}\)

 

[pka]

\(\mathcal{P}(M|+)=\dfrac{\mathcal{P}(+|M)\mathcal{P}(M)}{\mathcal{P}(+|M)\mathcal{P}(M)+\mathcal{P}(+|\neg M)\mathcal{P}(\neg M)}\)

I should have given Jim Pitman credit for this answer: see page 50, example #3 of his textbook PROBABILITY: that is almost the exact problem that has to do with false positives.