A certain company offers in-home cral HIV testing. According to their website, out of 4,998 persons who were unaware of their HIV status, 96 persons were HIV positive and 4,902 wer HIV negative (as determine by an independent lab test). For 4,901 out of e 4,902 persons who were HIV negative, the company's test correctly predicted such a negative result, but incorrectly predicted a positive result for the one remaining person. Of the 96 persons were HIV positive, the company's test correctlypedicted a positive result for 90 of them and a negative result for the others. These results can be summarized in the table below Pos Neg Total HIV 90 6 96 No HIV 1 4,901 4,902 Total 91 4,907 4,998 Estimate P(HIV|Pos) for the population that the sample of 4,998 people represents. (Round to four decimal places as needed.)

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Update:
A certain company offers in-home cral HIV testing.
According to their website, out of 4,998 persons
who were unaware of their HIV status, 96 persons
were HIV positive and 4,902 werc HIV negative (as
determine by an independent lab test). For 4,901
out of e 4,902 persons who were HIV negative,
the company's test correctly predicted such a
negative result, but incorrectly predicted a positive
result for the one remaining person. Of the 96
persons were HIV positive, the company's test
correctlypedicted a positive result for 90 of them
and a negative result for the others. These results
can be summarized in the table below
Pos
Neg
Total
HIV
90
6
96
No HIV 1
4,901 4,902
91
4,907 4,998
Total
Estimate P(HIV|Pos) for the population that the
sample of 4,998 people represents. (Round to four
decimal places as needed.)
Transcribed Image Text:Update: A certain company offers in-home cral HIV testing. According to their website, out of 4,998 persons who were unaware of their HIV status, 96 persons were HIV positive and 4,902 werc HIV negative (as determine by an independent lab test). For 4,901 out of e 4,902 persons who were HIV negative, the company's test correctly predicted such a negative result, but incorrectly predicted a positive result for the one remaining person. Of the 96 persons were HIV positive, the company's test correctlypedicted a positive result for 90 of them and a negative result for the others. These results can be summarized in the table below Pos Neg Total HIV 90 6 96 No HIV 1 4,901 4,902 91 4,907 4,998 Total Estimate P(HIV|Pos) for the population that the sample of 4,998 people represents. (Round to four decimal places as needed.)
Expert Solution
Step 1

Conditional probability formula :

P(A | B) = P(A n B)/P(B) 

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