How to calculate probability and conditional probability Estimates for the prevalence of Alzheimer’s

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How to calculate probability and conditional probability

Estimates for the prevalence of Alzheimer’s disease provided
by an observational study are listed below:

Prevalence of Alzheimer’s disease (cases per 100
individuals)

Age-group Males Females

65-69 13 05

70-74 33 21

75-79 49 38

80-84 75 82

85+ 283 223

Suppose four unrelated individuals (a 72 year-old man, an 81
year-old man, a 67 year-old man and an 87 year-old woman) are selected from a
community

a) According to the data in table above, what is the
probability that all four individuals have Alzheimer’s disease?

b) What is the probability that at least one of the men has
Alzheimer’s disease?

c) What is the probability that the woman and one of the men
have Alzheimer’s disease?

d) Suppose a married couple (a man and a woman in this case)
are both in their respective age groups of 75-79 An additional study shows
that the probability that both members of a married couple will have the
disease (where each member is 75-79 years old) is 0027

What is the probability that the woman will have Alzheimer’s
disease given that the man has Alzheimer’s disease?

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