Mental Health Estimates of the prevalence (probability) of certain disease have recently been provided. The estimates are given in the Table. Suppose an unrelated 77 year-old man, a 76 year-old woman, and a 82 year-old woman are selected from a community.
TABLE Probability of Alzheimer's disease
AGE GROUP MALES FEMALES
65-69 0.016 0.000
70-74 0.000 0.022
75-79 0.049 0.023
80-84 0.086 0.078
85+ 0.350 0.279
What is the probability that exactly one of the three people has Alzheimer's disease?
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?
Suppose we know two of the three people have Alzheimer's disease. What is the conditional probability that they are both women?
Suppose we know two of the three people have Alzheimer's disease. What is the conditional probability that they are both younger than 80 years of age?
Suppose the probability that both members of a heterosexual married couple, each of whom is 75-79 years of age, will have Alzheimer's disease is .0015. What is the conditional probability that the man will be affected given that the woman is affected? How does this value compare with the probability in the Table? Why should it be the same (or different)?
What is the conditional probability that the woman will be affected given that the man is affected? How does this value compare with the prevalence in Table 3.5? Why should it be the same (or different)?
What is the probability that at least one member of the couple is affected?