## Probability Calculation

Probability Calculation is a site that provides free tools that allow you to easily calculate probability. It refers to calculating the probability of an event "A" occurring when a trial with an occurrence probability of "x"% is performed "n" times.

## How to use

- Select the "Probability formula" you want to find.
- Enter the values needed for the calculation: "Occurrence probability (x) %", "Number of trials (n)", "Number of occurrences (k)", and "Occurrence probability (y) %".
- The "Probability calculation result value" will be calculated automatically.

## What is Probability?

Probability is a numerical representation of the likelihood that an event will occur. It is generally expressed in the range of 0 to 1, with 0 meaning "it will never happen" and 1 meaning "it will definitely happen". Probability is also often expressed as a percentage, in which case it is shown in the range of 0% to 100%.

Probability calculations are used in the following situations.

- Single trial probability: For example, the probability of rolling a "3" on a single roll of a dice is 1/6 (16.67%).
- Multiple trial probability: How often an event occurs over multiple trials, or the probability that it will occur at least once.

Probabilities are interpreted as follows:

- 0 (0%): The event will never occur.
- 1 (100%): The event will definitely occur.
- 0.5 (50%): The event occurs with a 50/50 chance.

## How to calculate probability

### Basic probability calculation

The probability of an event occurring can be calculated using the following formula.

**P(A)** = **Number of ways that event A occurs** / **Number of all possible ways**

### Probability of multiple independent events

When two or more events occur independently, multiply the probability of each event to get the overall probability.

**P(A and B)** = **P(A)** × **P(B)**

### Probability of multiple exclusive events

The probability of any one of the exclusive events (events that do not occur simultaneously) occurring is calculated by adding up the probabilities of each.

**P(A or B)** = **P(A)** + **P(B)**

### Conditional Probability

Used to calculate the probability that an event A occurs under the condition that an event B occurs.

**P(A | B)** = **P(A and B)** / **P(B)**

### Probability of repeated trials (binomial distribution)

To calculate the probability that an event occurs k times in n trials, use the following formula.

**P(X = k)** = **C(n, k)** p^{k} (1-p)^{n-k}

### Probability of occurrence at least once

To find the probability that an event will occur at least once in n trials, subtract the "probability of no occurrence at all" from 1.

**P(occurs at least once)** = 1 - (1 - p)^{n}

## Notes

This tool is available for free.

※This program is created and confirm the operation in PHP8.1.22.

※If you have any inquiries, opinions, or requests that you would like to make,
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