# The subject probability has been developed to a great

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The subject probability has been developed to a great extent and to-day, no discipline in social, physical or natural sciences is left without the use of probability. It is widely and popularly used in the quantitative analysis of business and economic problems; and is an essential tool in statistical inferences which form the basis for the decision theory. In other words, the role played by probability in

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5 modern science is of a substitute for certainty. Thus, the probability theory is a part of our everyday life. Definition The number of occurrences of a targeted event divided by the number of occurrences plus the number of failures of occurrences (this adds up to the total of possible outcomes): p(a) = p(a)/[p(a) + p(b)] 2.3.2. TERMINOLOGY The various terms which are used in defining probability under different approaches are discussed hereunder. 1) Random Experiment: - An operation which produces an outcome is known as experiment. If it is conducted repeatedly under homogeneous conditions and the result of which is not unique but may be any one of the various possible outcomes is called random experiment. In other words, an experiment is said to be random if we cannot predict the outcome before the experiment is carried. Ex. Tossing a coin. 2) Trial and Event : - Performing a random experiment is called a trial, and the outcome is referred to event. For Example, the result is not unique by tossing a coin repeatedly. We may get either head or tail. Thus, tossing of a coin is a random experiment and getting of a head or tail is an event. 3) Independent and Dependent Events : - If the occurrence of an event does not affect the occurrence of other, such event is said to be independent event. For example, in tossing a die repeatedly, the event of getting 3 in 1 st throw is independent of getting 3 in 2 nd , 3 rd or subsequent throws. Event is said to be dependent, if the occurrence of an event does affect the occurrences of other. For example, if we draw a single card from a deck of cards, probability of getting a king is 4/52. If we do not replace this card, the probability of a king occurring in the next draw will be affected. Probability of getting a king in the second is 3/51. Hence the event is dependent. 4) Mutually Exclusive Events : - Two or more events are said to be mutually exclusive if the occurrence of any one of them excludes the occurrence of all others. For example, if a die is cast, any outcome corresponding to any of the 6 faces exclusive the occurrence of remaining 5 faces in that trial. Hence, all the outcomes are mutually exclusive. 5) Equally Likely Events : - The outcomes are said to be equally likely or equally probable if none of them is expected to occur in preference to other. For example, if a coin is cast, the outcomes viz. head and tail are equally likely if coin is unbiased.
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