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Suppose an unrelated 77-year-old man, 76-year-old woman, and 82-year-old woman are selected from a community.

(a) What is the probability that all three of these individuals have Alzheimer's disease?

(b) What is the probability that at least one of the three people has Alzheimer's disease?

(c) Suppose we know one of the three people has Alzheimer's disease, but we don't know which one. What is the conditional probability that the affected person is a woman? The Chinese Mini-Mental Status Test (CMMS) consists of 114 items intended to identify people with Alzheimer's disease and senile dementia among people in China. An extensive clinical evaluation of this instrument was performed, whereby participants were interviewed by psychiatrists and nurses and a definitive diagnosis of dementia was made. The results obtained for the subgroup of people with at least some formal education. Suppose a cutoff value of = 20 on the test is used to identify people with dementia.

(a) What is the sensitivity of the test?

(b) What is the specificity of the test?

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