After him many authors in statistics had tried to remodel the idea given by the former. Sometimes statistical analysis becomes paralyzed without the theorem of probability.
The probability theory provides a means of getting an idea of the likelihood of occurrence of different events resulting from a random experiment in terms of quantitative measures ranging between zero and one.
The probability is zero for an impossible event and one for an event which is certain to occur. Let us clarify the meaning of probability with an example of drawing a playing card. The probability of an event stated or expressed mathematically called as a ratio. These ratios, called probability ratios, are defined by that fraction, the numerator of which equals the desired outcome or outcomes, and the denominator of which equals the total possible outcomes.
More simply put, the probability of the appearance of any face on a 6-faced e. Thus, a probability is a number or a ratio which ranges from 0 to 1. Zero for an event which cannot occur and 1 for an event, certain to occur. The classical approach to probability is one of the oldest and simplest school of thought. It has been originated in 18th century which explains probability concerning games of chances such as throwing coin, dice, drawing cards etc. According to him probability is the ratio of the number of favourable cases among the number of equally likely cases.
In this approach the probability varies from 0 to 1. When probability is zero it denotes that it is impossible to occur. From a bag containing 20 black and 25 white balls, a ball is drawn randomly. What is the probability that it is black. This approach to probability is a protest against the classical approach. If there are two types of objects among the objects of similar or other natures then the probability of one object i.
This type of probability approach though applied in business and economics area still then it is not a reliable one. The events are said to be mutually exclusive when they are not occurred simultaneously. Among the events, if one event will remain present in a trial other events will not appear.
In other words, occurrence of one precludes the occurrence of all the others. If a girl is beautiful, she cannot be ugly. If a ball is white, it cannot be red. If we take another events like dead and alive, it can be said that a person may be either alive or dead at a point of time.
But lie cannot be both alive and dead simultaneously. If a coin is tossed cither the head will appear or tail will appear. But both cannot appear in the same time. It refers that in tossing a coin the occurrence of head and tail comes under mutually exclusive events.
Two or more events are said to be independent when the occurrence of one trial does not affect the other. It indicates the fact that if trial made one by one, one trial is not affected by the other trial. And also one trial never describes anything about the other trials.
The events in tossing a coin are independent events. If a coin is tossed one by one, then one trial is not affected by the other. In a trial the head or tail may conic which never describes anything what event will come in second trial. So the second trial is completely independent to that of the first trial. Dependent events are those in which the occurrence and non-occurrence of one event in a trial may affect the occurrence of the other trials.
Here the events are mutually dependent on each other. If a card is drawn from a pack of playing cards and is not replaced, then in 2nd trial probability will be altered.
Events are said to be equally likely, when there is equal chance of occurring. If one event is not occurred like other events then events are not considered as equally likely. Or in other words events are said to be equally likely when one event does not occur more often than the others. If an unbiased coin or dice is thrown, each face may be expected to occur is equal numbers in the long run. The probability of an event is a number describing the chance that the event will happen.
An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero. If there is a chance that an event will happen, then its probability is between zero and 1. In probability, the probability of an event cannot be less than 0 and greater than 1. This is because the probability of an impossible event is 0, and the probability of a sure event is 1. NOTE :- A sure event is an event, which always happens.
The probability of a sure event has the value of 1. The probability of an impossible event has the value of 0.
Begin typing your search term above and press enter to search. Press ESC to cancel. Skip to content Home Essay What is the importance of statistics and probability in our daily life? Ben Davis May 13, What is the importance of statistics and probability in our daily life? Why probability and statistics are important in the business world?
What are the uses of probability in statistics? Where is probability used in daily life? What is probability in real life? What is the application of probability? What is the concept of probability? Which of the following is the best definition of probability? What is probability and its properties?
What is the biggest value that a probability can take? What are the 3 axioms of probability? The dice rolls 5 or 6 or any other value, the prior occurrence of 5 has nothing to do which the followed-up rolling of the dice. Dependent Event Dependent Events are a set of events that depend upon the occurrence of any of the Other.
The probability of occurrence of one event depends upon the occurrence of the other event. Thus, we call it dependent. The next outcome is dependent upon the prior.
Distributions Probability Distribution can be defined as a function that explains every possible value and possibility that a variable can output within a given range for any particular experiment.
Continuous Distribution Continuous Distribution explains the probabilities of occurrence of all the values within a given range in a particular experiment. Only, the range of values has a non — zero probability. In continuous Distribution, the probability of a continuous random variable equaling some value is always 0. It is often represented with the region under the curve. Discrete Distribution Discrete Distribution explains the probability of occurrence of every value of a discrete arbitrary variable.
In a discrete probability distribution, every possible value of the discrete random variable has a non-zero probability. Henceforth, a discrete probability distribution is mostly represented in a tabular form.
This theorem is named after the 18th-century British Mathematician Thomas Bayes, who discovered this theorem. This mathematical formula has been widely used in Machine Learning for Modeling Hypotheses, Classification, and Optimization. Let, 0. Though AI and Data Science are two different fields, there are lots of things that overlap, between the two. We need to understand the mathematics that goes behind the models we use for AI and Data Science. Basic Algebra acts as the backbone for all these different areas of Mathematics which are then used by Artificial Intelligence and Data Science.
How much statistics are necessary to know on an everyday basis? Probabilities help us realize if this problem can be solved with the tools and resources and data we have. Engineers make decisions with the information they have and thus, statistics and probabilities are important. So, Statistics and Probabilities are widely used from the inception of a project to firstly figure out the ways to solve the problem and to the end of completion of find the solution. Conclusion Today, we learned about Probabilities.
We learned what Probabilities are, how they are used in real life, and understood different types of Conditional Probabilities. One of the key things to take note of is the difference between Probability and Likelihood.
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