A medical test has been designed to detect the presence of a certain disease. Among people who have the disease, the probability that the disease will be detected by the test is 0.91. However, among those who do not have the disease, the probability that the test will detect the presence of the disease is 0.04. It is estimated that 4% of the population who take this test actually have the disease. (Round your answers to three decimal places.) (a) If the test administered to an individual is positive (the disease is detected), what is the probability that the person actually has the disease?(b) If the test administered to an individual is negative (the disease is not detected), what is the probability that the person actually does have the disease?
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.
A medical test has been designed to detect the presence of a certain disease. Among people who have the disease, the
(b) If the test administered to an individual is negative (the disease is not detected), what is the probability that the person actually does have the disease?
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