During the murder trial of O. J. Simpson, Alan Der-showitz, an advisor to the defense team, stated on television that only about 0.1% of men who batter their wives actuallymurder them. Statistician I. J. Good observed that even if, given that a husband is a batterer, the probability he is guilty of mur-dering his wife is 0.001, what we really want to know is the probability that the husband is guilty, given that the wife wasmurdered. Good estimates the probability of a battered wifebeing murdered, given that her husband is not guilty, as 0.001.The probability that she is murdered if her husband is guiltyis 1, of course. Using these numbers and Dershowitz’s 0.001probability of the husband being guilty, find the probabilitythat the husband is guilty, given that the wife was murdered.Source: Nature.
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.
During the murder trial of O. J. Simpson, Alan Der-
showitz, an advisor to the defense team, stated on television
that only about 0.1% of men who batter their wives actually
murder them. Statistician I. J. Good observed that even if, given
that a husband is a batterer, the probability he is guilty of mur-
dering his wife is 0.001, what we really want to know is the
probability that the husband is guilty, given that the wife was
murdered. Good estimates the probability of a battered wife
being murdered, given that her husband is not guilty, as 0.001.
The probability that she is murdered if her husband is guilty
is 1, of course. Using these numbers and Dershowitz’s 0.001
probability of the husband being guilty, find the probability
that the husband is guilty, given that the wife was murdered.
Source: Nature.
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