Suppose that the fraction of people in the US who are white is 40%, black is 15%

Question

Suppose that the fraction of people in the US who are white is 40%, black is 15%, and the other ethnicities are grouped together for the remaining 45%. The fraction of white people who have glaucoma at the age of 65 is 30%. The analogous fractions for blacks and others are 45% and 25%, respectively. For anyone who has glaucoma, the probability of having an abnormal intra-ocular pressure (IOP) reading is 65% and for someone who does not have glaucoma, the probability of an abnormal IOP reading is 15%.

Explanation / Answer

probabilty of IOP is normal and person is black are not statistically independent as event IOP is normal does depend on if person has glaucoma which further depends on ethnicities. Hence they are dependent.

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