Estimates of the prevalence of Alzheimer's disease have...

Estimates of the prevalence of Alzheimer's disease have recently been provided by Pfeffer et al. [8]. The estimates are given in Table $3.5 .$ Suppose an unrelated 77 -year-old man, 76 -year-old woman, and 82-year-old woman are selected from a community.What is the probability that at least one of the women has Alzheimer's disease?

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Key Concepts

Probability of Union of Events

The probability of the union of events involves finding the likelihood that at least one of several events occurs. When events are independent, this is often calculated using the complement rule by determining the probability that none of the events occur and subtracting that value from one.

Independence of Events

Independence of events means that the occurrence of one event does not affect the occurrence of another. When events are independent, the overall probability of several events not happening simultaneously is the product of each individual event’s probability of not occurring.

Complement Rule in Probability

The complement rule is a foundational concept in probability which states that the probability of an event occurring is equal to one minus the probability of the event not occurring. This concept simplifies calculations especially when finding the probability of 'at least one' event happening.

Prevalence Rate

The prevalence rate is the proportion of individuals in a population who have a particular condition at a specified time. It is significant in epidemiology because it quantifies the disease burden and is used in calculating the likelihood or risk that an individual or a group from the population might have the disease.

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