Adding Probabilities
Adding Probabilities
Two events are called as an independent event, if both do not depend on each other;
means when we calculate probability of one event, then the other event does not
effects the probability of that event. Now we will discuss how we add two Independent
Events:
For adding probabilities of two independent events, we use fol owing steps -
Step 1: First of al , we evaluate probability of each event, like we have two independent
events `A' and `B', then we calculate probability of event `A' and probability of event `B'.
Step 2: After calculation of probability, we perform `AND' operation between the given
probabilities by using the multiplication operation between the given probabilities because
the given independent probabilities do not depend on each other and we use "^" symbol
for representation of `AND' operation like -
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Probability is ordinarily used to describe an attitude of mind towards some proposition of
whose truth we are not certain.
The proposition of interest is usual y of the form "Wil a specific event occur?" The attitude
of mind is of the form "How certain are we that the event wil occur?" The certainty we
adopt can be described in terms of a numerical measure and this number, between 0 and
1, we cal probability.
The higher the probability of an event, the more certain we are that the event wil occur.
Thus, probability in an applied sense is a measure of the confidence a person has that a
(random) event wil occur.
The concept has been given an axiomatic mathematical derivation in probability theory,
which is used widely in such areas of study as mathematics, statistics, finance, gambling,
science, artificial intel igence/machine learning and philosophy to, for example, draw
inferences about the expected frequency of events.
Probability theory is also used to describe the underlying mechanics and regularities of
complex systems.
The word probability does not have a singular direct definition for practical application. In
fact, there are several broad categories of probability interpretations, whose adherents
possess different (and sometimes conflicting) views about the fundamental nature of
probability. For example:
Frequentists talk about probabilities only when dealing with experiments that are random
and wel -defined. The probability of a random event denotes the relative frequency of
occurrence of an experiment's outcome, when repeating the experiment. Frequentists
consider probability to be the relative frequency "in the long run" of outcomes.
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Subjectivists assign numbers per subjective probability, i.e., as a degree of belief.
Bayesians include expert knowledge as wel as experimental data to produce
probabilities. The expert knowledge is represented by a prior probability distribution. The
data is incorporated in a likelihood function.
The product of the prior and the likelihood, normalized, results in a posterior probability
distribution that incorporates all the information known to date.
Probability theory is applied in everyday life in risk assessment and in trade on commodity
markets. Governments typical y apply probabilistic methods in environmental regulation,
where it is cal ed pathway analysis.
A good example is the effect of the perceived probability of any widespread Middle East
conflict on oil prices--which have ripple effects in the economy as a whole. An
assessment by a commodity trader that a war is more likely vs. less likely sends prices up
or down, and signals other traders of that opinion.
Accordingly, the probabilities are neither assessed independently nor necessarily very
rationally. The theory of behavioral finance emerged to describe the effect of such
groupthink on pricing, on policy, and on peace and conflict.


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