A screening procedure for HIV is applied to a population which is at high risk f

Question

A screening procedure for HIV is applied to a population which is at high risk for HIV-10% of this population are believed to be HIV positive. The screening test is positive for 90% of people who are genuinely HIV positive, and negative for 85% of people who are not HIV positive. What are the probabilities of false positive and false negative results? In a bag there are 6 balls of unknown colors. Three balls are drawn without replacement and are found to be black. Find the probability that no black ball is left in the bag. The rock strata A and B are difficult to distinguish in the field. Through careful laboratory studies it has been determined that the only characteristic which might be useful in aiding discrimination is the presence or absence of a particular brachiopod fossil. In rock exposures of the sire usually encountered, the probabilities of fossil presence are found be as in the following table. It Is also known that rock type A occurs about four times as often as type B in this area of study.

Explanation / Answer

10 % of the population are believed to be HIV positive.

Test is positive for 90% of people who are genuinely HIV positive

Test is negative for 85% of people who are not HIV positive

Let the total population be x

the people with HIV positive = 0.1x

total people without HIV = 0.9x

According to the test the total people who dont have HIV but are screened as HIV positive =0.9 x 0.15 = 0.135x

(as 85% of them are correctly screened and 15% are incorrectly screened)

Therefore probability of false positive = 0.135x/x = 0.135

According to the test the total people who have HIV but are screened as HIV negative= 0.1x * 0.1= 0.01x

Therefore probability of false negative = 0.135x/x = 0.01

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