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Maths / Probability / Probability of An Event

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Probability of An Event

Definition of Probability:

Probability is considered as a branch of mathematics that deals with uncertainty. It has been developed out of practical considerations and is used in taking decisions in almost every field. For example, while going out of house on cloudy day we have to take decision whether we should carry an umbrella or not. Such type of decision is taken by taking into consideration the probability of the occurrence of the event.

Let n be the total number of trials and m be the total number of trials in which the event has happened. The empirical probability P(E) of an event to occur is defined as:

$P(E)=frac{Number ;of ;trials; in; which; the; event; happened}{The; total; number; of; trials}=frac{m}{n}$

$0leq mleq n;;Rightarrow 0leq frac{m}{n}leq 1;;Rightarrow 0 leq P(E)leq 1$
As the number of favorable trials will always be less than the total trials, so the probability of an event to occur will always be less than 1.

Illustration: An experiment was done 250 times in a day. 150 outcomes from the experiment were favorable, what is the probability that the next outcome is favorable.

Solution: Total number of trials = 250

No of favorable trials= 150

$dpi{110} P(E)=frac{Number ;of ;trials; in; which; the; event; happened}{The; total; number; of; trials}=frac{150}{250}=frac{3}{5}$

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