Probability Calculator – Introduction

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What is meaning by probability?

In simple words, probability means that it is an aspect through which we can measure as to when an event will occur. It is also quantified to be a number between 0 as well as 1. Here, 0 means that it is impossible while certainty is represented by 1. If the probability of some event is stated to be high then there are more chances that an event shall occur.

Probability Calculator

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Where is probability term used?

Essentially the term probability & things related to it are widely used in areas such as mathematics / statistics / finance / science & physics to be specific / machine learning / computer science / artificial intelligence / game theory / philosophy. In addition to this, the probability theory is stated to be put in use in order to describe underlying mechanics as well as the regularities of the complex systems.

Origin of the word – probability

The term probability has been derived from the Latin word, probabilitas which in other words mean probity or a measure of authority of witness especially in a legal case in Europe. And this word is at times co – related with a witness’s ability.

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How to calculate probability?

  1. To calculate the probability of a random event the following formula of probability is put in to use –

Probability =\( \frac{event \quad \quad (\quad \quad or \quad \quad events)}{number \quad \quad \quad of \quad \quad \quad outcomes}\)

How to calculate the mathematical probabilities?

  1. Probability of an independent event formula is –

\(p = \frac{n_{e}}{n}\)

Here P is the probability while  is the distinctive & the likely outcomes whereas  is the number of distinctive outcomes which represent occurrence of event.

  1. Probability of independent events occurring at the same time formula is –

Probability = \(p_{{1}} \times p_{{3}} \times p_{{2}}\)

  1. Probability formula –

\( probability \, = \, \frac {number\, of\, favourable\, outcomes}{number\, of\, possible\, outcomes}\)

In the above equation, the favourable outcome can be stated to be an event which an individual may perhaps be looking forward to which will most probably take place.

  1. Probability of the normal distribution formula

As far as the probability theory is concerned then the normal distribution which is also known as the Gaussian distribution turns out to be quite a common continuous probability distribution. These normal distribution moreover happens to play an important role in statistics & even are made use of especially in the natural as well as social sciences specifically to represent the real – valued random variables where the distribution is unknown.

The formula for the probability density of the normal distribution has been mentioned below –

\( f(x|\mu,\sigma^{2})\, = \, \frac{1}{\sqrt{2 \sigma^{2} \pi}}e^{- \frac {(x- \mu)^{2}}{2 \sigma^{2}}}\)

In the above equation, is nothing but the expectation or the mean of the distribution & it is also said to be the mode as well as the median. While on the other hand,  is stated to be the standard variation while  is nothing but the variance. Furthermore, this random variable along with the Gaussian distribution is stated to be normally distribution hence it is known as the normal deviate.

How to use a probability calculator?

To make use of a probability calculator, enter the values of mean, standard deviation & others before clicking on calculate.