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# How to calculate probability and conditional probability

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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 1.3 0.5
70-74 3.3 2.1
75-79 4.9 3.8
80-84 7.5 8.2
85+ 28.3 22.3

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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The solution provides the detailed explanation how to find the probability and conditional probability.

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(a) all four individual have Alzheimer's disease (they are independent events)
P=P(72male, 3.3%)*P(81male,7.5%)*P(67male, 1.3%)*P(87female, 22.3%)=3.3%x7.5%x1.3%x22.3%=7.175e-4%

(b)First, we calculate the probability of "none of the ...

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