2. Estimates of the prevalence of Alzheimer's disease are given in Table below. 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 women has Alzheimer's disease? c. What is the probability that at least one of the three people has Alzheimer's disease? d. What is the probability that exactly one of the three people has Alzheimer's disease? e. 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? f. Suppose we know two of the three people have Alzheimer's disease. What is the conditional probability that they are both women? g. 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? Table 1 Prevalence of Alzheimer's disease (cases per 100 population) Age group Males Females 65-69 1.6 0.0 70-74 0.0 2.2 75-79 4.9 2.3 80-84 8.6 7.8 85+ 35.0 27.9
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
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