# Probability Calculator

Probability calculator helps you to find the probability of a single event or multiple events. Just select an event, input your values to check the probability.

Single Probability Calculator
Number of possible outcomes
Number of events occurred

Multiple Event Probability Calculator
Number of possible outcomes
Number of events occur in A
Number of events occur in B

## What is Probability?

In simple words, the probability is defined as how likely something could happen and what are chances a proposition is true or false. It is the part of a branch of mathematics called statistics. Probability is widely used when the occurrence of an event is uncertain.

The three major types of probabilities are:

1. Theoretical Probability

2. Experimental Probability

3. Axiomatic Probability

## Difference Between Axiomatic, Experimental, and Theoretical Probability

The occurrence of a given event’s likelihood is known as probability. Over here, we would get to know about the difference between axiomatic, experimental, and theoretical probability.

## Axiomatic Probability

Axiomatic probability is just another way of describing an event’s probability. The word itself defines the nature of the methodology that is used to calculate the probability. While opting for this approach, some predefined axioms are used before assigning the probabilities. The approach is used for quantizing the event and ultimately eases the calculation of occurrence and non-occurrence of a particular event.

## Experimental Probability

Experimental probability deals with simulating the real event and the ratio of various possible outcomes during the experimental trials. It shows how often a given possibility is likely to take place.

### Theoretical Probability

The theoretical probability is quite different from both of the aforementioned methods. The theoretical methods don’t need to conduct experiments or deploy trial periods. In this case, the situation needs to be determined before finding the occurrence or non-occurrence of a particular event. In simple words, it is defined as the ratio of numbers of promising results to the number of possible results.

## How to Calculate Probability?

The calculation of probability involves the segregation of a problem into individual probabilities and multiplying the chances of occurrence with one another. The problems falling under the probability format can be calculated easily by following the steps mentioned below.

Step 1

First of all, you have to determine the probability of the event that at least has one possible outcome. For instance, you can determine the possible outcomes of getting heads on a coin because you either get heads or don’t get heads.

Step 2

The next step is the identification of the total number of outcomes for the event determined in the previous step. In the event of flipping a coin, the total number of outcomes is 2, which are heads and tails.

Step 3

The last step is to divide the possibility of an event’s occurrence with the total number of outcomes. Continuing with the same example, the possible number of times we can get heads after flipping a coin is 1, and the total number of outcomes is 2. Hence, the probability of getting heads would be calculated as 1/2, i.e., 0.5.

## How to Calculate Probability of a Single Event Using Probability Calculator?

The usage of our conditional probability calculator for the calculation of a single event’s probability doesn’t involve any intricacies. You can make use of this online probability calculator by following the easy steps mentioned below.

• Click on the "Single" button for the calculation of single event probability.
• Enter the number of possible outcomes.
• Enter the number of events that occurred.
• Click the "Calculate Probability" button. The results will be displayed in a matter of seconds.

## How to Find Probability of Multiple Events Using Probability Calculator?

Duplichecker.com has made it easier for the people to find the probability of multiple events as its calculation is a bit different from the ordinary or single event’s probability. After accessing the statistics probability calculator on our site, follow the steps mentioned below:

• Click on the Multiple button to access the probability calculator multiple events.

• Enter the number of possible outcomes

• Enter the number of events that occurred in A and B.

• Hit the Calculate Probability button. The results will be displayed on your screen in a blink of any.

## How to Find Probability of Multiple Events Using Probability Calculator?

Duplichecker has made it easier for people to find the probability of multiple events as its calculation is a bit different from the ordinary or single event’s probability. After accessing the statistics probability calculator on our site, follow the steps mentioned below:

• Click on the “Multiple” button to access the probability calculator multiple events.
• Enter the number of possible outcomes
• Enter the number of events that occurred in A and B.
• Hit the “Calculate Probability” button. The Probability Calculator gives you the results that will be displayed on your screen in the blink of any.
• ## The Intersection of A and B

The intersection of A and B can be defined as all of the elements that exist in both sets A and B.

The intersection of A and B, in statistics problems, is written as A∩B.

For instance, if set A contains {a,b,c,d,e,f,g} and set B contains {b,f,h}, what will be A∩B?

The terms that exist in both sets are b and f. Hence, A∩B = {b,f}

## Union of A and B

The union of A and B is the combination of two sets containing all the elements in either of the sets. The union of A and B can be written as A∪B. An example for the union of A and B could be:

A = {1,2,3,4,5,6}

B = {2,4,9,10}

The A∪B for this example would be A∪B = {1,2,3,4,5,6,9,10}

## Conditional Probability Formula of A and B

The conditional probability is the calculation of the event’s A probability, given that event B has occurred. The probability of an event formula to define the conditional probability of A and B is:

P(A|B) = P(A∩B) P(B).

Note: You can also calculate probability with this Conditional Probability calculator.

## How to find Experimental Probability Manually with Experimental Formula?

The calculation of experimental probability relies on trials. Firstly, an experiment is carried out, and results are recorded, then these results are used to calculate the experimental probabilities. Below you’ll come across the formula of experimental probability.

Probability of an Event P(E) = number of times an event occurs / total number of experiments

Let’s get to know how experimental probability works with the help of an example.

Three friends, Aaron, Peter, and Mathew, are asked to toss a coin 15 times, and the outcome of the experiment is mentioned in the table below.

Coin Tossed By No. of. Heads No. Of. Tails
Aaron 6 9
Peter 7 8
Mathew 8 7

Now, we need to calculate the occurrence of heads and tails in this experiment. The formula that would be applied is mentioned below:

Experimental Probability heads occurrence = Number of times head occurs / the number of times coin is flipped.

&

Experimental Probability tails occurrence = Number of times tails occurs / the number of times coin is flipped.

Coin Tossed By No. Of. Heads No. Of. Tails Experimental Probability for the Head occurrence Experimental Probability for the Tail occurrence
Aaron 6 9 6/15 = 0.4 9/15 = 0.6
Peter 7 8 7/15 = 0.47 8/15 = 0.53
Mathew 8 7 8/15 = 0.53 7/15 = 0.47

It depicts that when the number of tosses of coin increases, then the probability of occurrence of tail and head reaches the point of 0.5.

## Calculate Theoretical Probability with Probability Calculator

Theoretical probability calculator by DupliChecker provides you to inspect the relationship of likelihood in two separate or distinct events. You will need to provide an event that has at the minimum one possible outcome. You will further need to identify the total possibilities that took place. At last, the total number of an event taking place will be divided by the total number of outcomes. Therefore, the theoretical probability calculator available on Duplichecker.com will generate accurate results as per the mathematical formulas.