Table of Contents

**Introduction **

Consistently we go over different circumstances in life whenever we have to take a risk or chance. In view of potential results, we settle on our choice. The investigation of these odds is the thing that we called probability.

Likelihood clarifies how likely prepositions can be valid or bogus. As we are probably aware of how the event will occur and what will be the expected outcome are difficult to communicate, yet with the assistance of probability, we can almost certainly tell how they happen. While determining the likelihood of any events, We face questions like these –

*What is the possibility that the event will occur? *

*Is one event can affect other events? *

*How to measure probability effectively?*

*Is there any tool or calculator to measure probability?*

Probability helps to answer these questions with ease as there are ways to calculate the probability of the event. Let us explore it together!

**Meaning **

It is one of the cardinal branches of mathematics and an important topic in data. In short, probability means possibility. It is the likelihood of the event to occur. The event can happen anytime and anywhere, so probability helps in predicting certain events. Many events can be uncertain, which can only be forecasted.

For Example – if you toss a coin in the air, you will get Head or Tail; we can predict the possible outcomes but cannot predict the exact result.

From the above definition, the following points are surfaced –

- The probability of the event is denoted from the range 0 to 1
- Sample points and space is equal to 1
- P(A) is referred to as the probability of an event A

But what if Event A doesn’t occur? In that case, P(A) will be close to zero, and if event A occurs, P(A) will be close to 1.

The formula of probability is –

**P(A) = n(A)/n(S)**

Where,

- P(A) – the probability of an event A
- n(A) – number of favorable outcomes
- n(S) – total number of events

Theoretically, it is expressed as the possibility of an event to happen is equal to the ratio of the number of favorable possibilities and the total number of outcomes.

**Types of Probability **

The three types of probability are as follows –

**Theoretical Probability**

As the name suggests, to find out the probability of the event, we try to know about the situation to identify the probability of the event. In other words, it is the ratio of the number of favorable outcomes to the number of possible outcomes.

**Probability of Event P(E) = No. of Favorable outcomes/ No. of Possible outcomes.**

**Experimental Probability**

Here, to find out the probability of the event, we rely on the experiment and recording of the occurrence of the event. It is also called an empirical probability. It is the ratio of the number of times that event occurs to the total number of trials.

**Probability of Event P(E) = No. of times that event occurs/ Total number of trials**

**Axiomatic Probability**

One of the ways to define probability is through axiomatic probability. Here, few axioms are predefined before predicting the outcome of any event. The event is quantified that makes it easy to calculate the expected outcome.

**Probability Tree **

It helps to apprehend and visualize various possible outcomes. Branch and ends are two crucial parts of the tree. With the help of the tree, you can decide when to add and when to multiply.

**Importance in probability in Statistics**

- It plays an important role in research investigation as predictions and estimates are a foundation base of research. By using a statistical method, one can make further analysis of the investigation and derive a conclusion.
- Probability assists in the decision-making process. Big organizations are outrightly dependent on the probability of making decisions about the future.
- It helps to control and cover the occurrence of any uncertain events or accidents. This method is widely used by insurance companies to craft their policy and decide their premium rates.
- Before adopting any statistical procedures, one must adhere to the theory of probability.

**Important terminology in probability **

**Mutually exclusive event –**When the event doesn’t occur simultaneously, it is called a mutually exclusive event that means one event can occur at one time in a trail. Two events can’t take place together. For Example – Either you will pass or fail the exam.**Independent and dependent event**– When the occurrence of one event doesn’t affect the other events in a trail, it is called independent and vice versa.**Equally likely events-**When there are equal chances of events to occur, it is called equally likely events that means if one event doesn’t occur, then we can reply to other events and so on.

**Ways to calculate Probability in Statistics **

Probability is a part of mathematical calculation that has a plethora of applications. Whether you want to measure the sales growth of your organization or identifying the chances of generating new customers for your business, the probability is there at your disposal. When something is likely to occur, we use probability. Let us explore the three different ways to calculate the probability in Statistics –

**Calculate the probability of the single random event**

**Identify the event with mutually exclusive outcomes –**Whenever you have to calculate probability, either the event should occur or shouldn’t. There should always be one condition as two things cannot take place at the same time. For Example – rolling a 3 in a die to win is a classic instance of the mutually exclusive event.**Figure out all the possible outcomes or events-**In most cases, there are chances that the outcome can be more than one. It is crucial to orient oneself with the desirable outcome whose probability needs to be calculated. For example – in the box, there are 12 red stones, 10 black stones, and 15 blue stones. If drawn out randomly, there is the probability that stones can be red or blue. Getting a red stone is our event, and the number of outcomes is the total stones in the box.**Divide the number of the event by the number of outcomes –**Dividing this will proffer the probability of the single event. For Example – The total number of the event is 2 and, the total number of outcomes is 8; it will be denoted as 4.**Calculate all the event possibilities-**Here, the possibilities of all the events need to add to 1 or 100%. In case the event doesn’t match with 1, you need to re-check your statistics as you might be missing some possible events.**Denote the probability of impossible sequels –**When there are no chances of any event occurring or anything that can’t happen. It has zero probability. For Example – Christmas only takes place on 25th December and, not on any other date.

**Calculate the probability of the multiple random events**

**Apprehending probability individually to calculate independent events –**Once you know the possibilities, calculate each separately to avoid the interference of one on another. They are called independent events because they don’t affect each other.**Take into consideration the prior effect of the dependent event-**If one event can affect the outcome of other events, you can measure the probability of events that are dependent on each other.**Multiply the expected probabilities separately by one another –**Whether the event is dependent or interdependent, probability can be calculated by multiplying the event by one another. You will get the probability of multiple events happening one after another.

**Converting odds to probability**

**Put positive results as numerator and odds as a ratio-**Here, the odds of the event will be the ratio of the event that may occur, and positive events can be set as the numerator for the same.**Add up the numbers before converting**– This is simple yet effective. Firstly, you need to divide the odds into two different events then add up the numbers to get the total outcomes.**Identify odds while calculating for a single event –**You have determined that there is a sum of 20 prospects and that 11 of those results are drawing a white stone. Along these lines, the likelihood of drawing white stones would now be able to be moved toward like some other single-event probability. Divide 11 (number of positive results) by 20 (number of complete functions) to get the likelihood.

**Conclusion **

From the above discussion, it is clear that probability is the process of identifying the occurrence of the event or the likelihood of any specific event. Probability is one of the topics in data. To know more, check out Data tips and Tricks as it offers the best learning platform** **that** **encourages students to develop and understands mathematics concepts easily and in a unique way that gets instilled in their minds for a longer period.

We hope you understand the concepts of probability and if you have any query, please comment down below, we would be more than happy to address it. Happy Learning!