The victims of a certain disease being treated at Wake Medical Center are classified annually as follows: cured, in temporary remission, sick, or dead from the disease. Once a patient is cured, he is permanently immune. Each year, those in remission get sick again with probability 0.17, are cured with probability 0.18, die with probability 0.05, and stay in remission with probability 0.6. Those who are sick are cured with probability 0.05, die with probability 0.2, go into remission with probability 0.4, and remain sick with probability 0.35. Find the transition matrix and do the calculations necessary to answer the following questions. (Give your answers correct to three decimal places.) (a) If a patient is now in remission, what is the probability he is still alive in two years? (Hint: In which states is a patient alive?) (b) If a patient is now in remission, what is the probability he dies within three years?
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.
The victims of a certain disease being treated at Wake Medical Center are classified annually as follows: cured, in temporary remission, sick, or dead from the disease. Once a patient is cured, he is permanently immune. Each year, those in remission get sick again with
Find the transition matrix and do the calculations necessary to answer the following questions. (Give your answers correct to three decimal places.)
(a) If a patient is now in remission, what is the probability he is still alive in two years? (Hint: In which states is a patient alive?)
(b) If a patient is now in remission, what is the probability he dies within three years?
(c) On average, how many years will a patient in remission live before being cured or dying from the disease?
years
(d) If a patient is presently sick, what is the expected number of years before the patient is cured or dies?
years
(e) What is the probability that someone who is currently in remission will eventually be cured?
(f) What is the probability that someone who is currently sick will eventually be cured?
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