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# Probability and Statistics: Definition, Formulas & Examples

## Probability

Probability is an important topic in mathematics in which it deals with predicting the likelihood of an incident. Commonly, all the events don’t happen in the same way as predicted. So, the best thing one can do is, try to predict how likely they can happen, with the help of ideas of probability. Probability deals with the consequences of mathematical definitions and real-world entities.

The probability of an event can easily be expressed as 0 and 1. In this, 0 indicates that the chances of that particular incident to occur are zero, or in simple words, the event is impossible to occur. In the meantime, 1 indicates the certainty of an incident. If the amount of probability is higher, it vividly means the event will likely occur.

For instance, tossing a coin containing two sides or faces means there are only two possible outcomes. It is either heads or tails. In this scenario, the probability of obtaining heads is the same as the probability of getting tails. There are no other possible results other than these two. So, the probability of attaining heads is ½ or 0.5 out of 1. In terms of percentage, it is 50 %. The same goes for tails as well.

The following is the formula for the probability of an event that is happening,
P (A)=(Total number of ways event A can occur) / (Total number of possible outcomes)

In easy terms, probability can be described as the total number of occurrences of a targeted event divided by the sum of occurrences in addition to the total amount of failures.
P(A)=P(a) / [P( a)+P( b)]

## Statistics

Statistics is a branch of mathematics that analyses a given set of real-life data or studies that utilise quantified models, synopses, assumptions, and representations to reach the results. Statistics include basic concepts such as mean, median, mode, skewness, kurtosis, variance, standard deviation, regression analysis and variance analysis.

Statistics is capable of summarising a process that can be simply used to characterise a dataset. If the dataset depends on a sample of a higher population, then we can easily develop interpretations regarding the population. The population is primarily based on the statistical outcome from those samples. This analysis requires the process of gathering, reviewing, data evaluation and summarisation into a mathematical form. Thus, statistics is a great source to analyse large volumes of data and their properties.

Statistics can be utilised in various professions, including manufacturing, medical, healthcare, production house, business, social works, psychology, humanities and government sectors etc. The data required for statistics can be effortlessly gathered using a sample procedure. The two types of statistical methods used in data analysis are descriptive statistics and inferential statistics.

The following are some of the common symbols used in probability and statistics:

Symbol Meaning Example
P (A ∩ B) Intersection P A ∩ B = 0.75
P (A ∪ B) Union P (A ∪ B) = 0.30
P (A | B) Conditiona P (A | B) = 0.56
var (X) Variance var (X) = 4
σ X Standard Deviation σ X= 4
M Population Mean = 40
2 Variance 2 = 16
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