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Sagot :
By using Probability, it can be calculated that
a) Probability that the person test positive for HIV is infected with HIV = 0.54
b) Probability that the person test positive for HIV is not infected with HIV = 0.46
c) Probability that the person test negative for HIV is infected with HIV = 0.0056
d) Probability that the person test negative for HIV is not infected with HIV (P(not HIV|-ve)) = 0.9944
What is Probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Probability that the person is infected with HIV (P(HIV)) = 0.08
Probability that the person is not infected with HIV (P(not HIV)) = 0.92
Probability that the person infected with HIV test positive (P(+ve|HIV)) = 0.94
Probability that the person infected with HIV test negative (P(-ve|HIV)) = 0.06
Probability that the person not infected with HIV test positive (P(+ve|not HIV)) = 0.07
Probability that the person not infected with HIV test negative (P(-ve|not HIV)) = 0.93
By using Baye's Theorem of probability,
a) Probability that the person test positive for HIV is infected with HIV (P(HIV|+ve)) =
[tex]\frac{0.94 \times 0.08}{0.94 \times 0.08 + 0.92 \times 0.07}[/tex] = 0.54
b) Probability that the person test positive for HIV is not infected with HIV (P(no HIV|+ve)) = 1 - 0.54 = 0.46
c) Probability that the person test negative for HIV is infected with HIV (P(HIV|-ve) =
[tex]\frac{0.06 \times 0.08}{0.06 \times 0.08 + 0.93 \times 0.92}[/tex] = 0.0056
d) Probability that the person test negative for HIV is not infected with HIV (P(not HIV|-ve)) = 1 - 0.0056 = 0.9944
To learn more about probability, refer to the link-
https://brainly.com/question/13604758
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Complete Question
Suppose that 8% of the patients tested in a clinic are infected with hiv. furthermore, suppose that when a blood test for hiv is given, 94% of the patients infected with hiv test positive and that 7% of the patients not infected with hiv test positive. what is the probability that
a) The person test positive for HIV is infected with HIV
b) The person test positive for HIV is not infected with HIV
c) The person test negative for HIV is infected with HIV
d) The person test negative for HIV is not infected with HIV
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