Problem 48 Refer to Problem 47 It is estimated that 016 of t

Problem 4.8. Refer to Problem 4.7. It is estimated that 0.16% of the adult population in this country without tuberculosis is infected with HIV. (a) Compute the probability that a randomly selected adult is infected with HIV. (b) Given that a randomly selected adult is infected with H IV, compute the probability that this adult is co - infected with tuberculosis.

Solution

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A)

Here,

P(HIV and no tub) = P(no tub) P(HIV|no tub) = (1-0.08)(0.0016) = 0.000128

Thus,

P(HIV) = P(HIV and Tub) + P(HIV and no tub) = 0.000036 + 0.000128 = 0.000164 [ANSWER]

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P(HIV and tub | HIV) = P(HIV and tub) / P(HIV) = 0.000036 / 0.000164 = 0.291512 [ANSWER]