Question 1151389
We are given this info:
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Chances a person with the disease tests positive = 0.90 [GIVEN]
Chances a person with the disease tests negative = 0.10 
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Chances a person without the disease tests positive = 0.10 
Chances a person without the disease tests negative = 0.90 [GIVEN]
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It is also given that the person chosen at random tests positive for the disease, so we are only concerned with:
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Chances a person with the disease tests positive = 0.90
Chances a person without the disease tests positive = 0.10
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We also know that only 1% of the population actually has the disease, so the above needs to be weighted as such:
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Chances a person with the disease tests positive = 0.90 * 0.01 = 0.009
Chances a person without the disease tests positive = 0.10 * 0.99 = 0.099
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We want to find the probability that the random person who tested positive actually has the disease, so we compute that as such:
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{{{0.009/(0.009 + 0.099)}}} = {{{0.009/0.108}}} = 0.0833