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# Probability Calculator

Probability calculator finds the probability of an event occurring by calculating the ratio of the favorable outcomes to the total outcomes. Probability is a field of statistics that is used to describe the likelihood of occurrence of an event.

## What is a Probability Calculator?

Probability Calculator is an online tool that helps to determine the chance of occurrence of an event. Probability can be classified into two types, namely, experimental probability and theoretical probability. Probability is used in several industries for building predictive mathematical models. To use this **probability calculator**, enter values in the input boxes.

### Probability Calculator

**NOTE: **Enter values upto 5 digits only.

## How to Use Probability Calculator?

Please follow the below steps to find the probability using the online probability calculator:

**Step 1:**Go to Cuemath’s online probability calculator.**Step 2:**Enter the favorable outcomes and the total number of outcomes in the input boxes of the probability calculator.**Step 3:**Click on the**"Calculate"**button to find the probability of an event.**Step 4:**Click on the**"Reset"**button to clear the fields and enter new values.

## How Does Probability Calculator Work?

The formula for theoretical probability is given as follows:

Theoretical Probability = Number of favorable outcomes / Total number of outcomes.

There are certain axioms that are followed by both theoretical probability as well as experimental probability. These are given as follows:

- The probability of any event will always be greater than or equal to 0.
- The set of all the outcomes possible for the event is given by the sample space.
- Suppose we have two events, A and B, that cannot occur at the same time. The probability of A or B occurring is given by the summation of the probability of A and probability of B. Further, such events are known as mutually exclusive events.

The rules of probability are given below:

- The null set is used to denote the probability of an impossible event.
- The probability of occurrence of an event lies between 0 to 1.
- An event cannot have a negative probability.
- The sum of the probability of an event happening and not happening is given by 1.

## Solved Examples on Probability Calculator

**Example 1:**

What is the probability of selecting a black ball from a bag containing 4 yellow balls, 6 blue balls, 8 red balls, and 3 black balls? Verify it using the probability calculator.

**Solution:**

Total number of possible outcomes = 21

Favorable outcomes = 3

Probability = 3/21

Probability = 1/7 = 0.14

Thus, the probability of selecting a black ball from the given bag is 1/7 or 0.14.

**Example 2:**

If we toss a coin once, what is the probability of getting heads? Verify it using the probability calculator.

**Solution:**

Total number of possible outcomes = 2

Favorable outcomes = 1

Probability = 1/2

Probability = 0.5

Thus, the probability of getting heads is 0.5.

Similarly, to find the probability of an event, you can try the probability calculator for the following:

- Find out the probability of getting a chocolate if a bag contains 10 chocolates and 5 toffees.
- What is the probability of getting 6 as a number when a dice is rolled?

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