Malaria Percentages Question

[furqan123]

plzz help

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?

 

[Deleted member 4993]

plzz help

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?

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[HallsofIvy]

plzz help

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?

Imagine a population of 100000. 1.5%, 1500, actually have malaria, the other 98500 do not. Of the 1500 who have malaria, 85%, 1275, test positive. Of the 98500 where do not have malaria, 10%, 9850, also test positive. That is a total of 1275+ 9850= 11125 who test positive, 1275 of whom actually have the disease. A little surprising, isn't it?

 

[Steven G]

@HallsofIvy: I am assuming that you are saying that the answer to the OPs question is the ratio of the numbers you found. But doesn't it matter that Ali showed symptoms of malaria? That is Ali is not a random person off the street taking the test

 

[HallsofIvy]

We are not told any probability that a person who "shows symptoms" has the disease so we cannot use that. Ali is among the 11125 who tested positive. Of those, 1275 actually have the disease. Given that Ali tested positive, the probability he has the disease is \(\displaystyle \frac{1275}{11125}\).