Probability Calculator

There are countless situations for the probability calculation. The following are two of the most common situations.

Probability of Normal Distribution

To find the probability area P for the normal distribution as well as finding out the confidence intervals table. Use -inf for negative infinite value and inf for positive infinite value.

Mean: (µ)
Standard Deviation (σ):
Left Bound (Lb): negative infinite use -inf
Right Bound (Rb): positive infinite use inf

Probability of Two Events

To find out the union, intersection, and other related probabilities of two events.

Probability of event A: P(A) a number between 0 and 1
Probability of event B: P(B) a number between 0 and 1

RelatedStandard Deviation Calculator | Sample Size Calculator | Statistics Calculator


Probability of Normal Distribution

The normal distribution or Gaussian distribution is a continuous probability distribution that follows the function of:

where µ is the mean and σ2 is the variance. If µ = 0 and σ2 = 1, it is called standard normal. The diagram above is a typical normal distribution curve.

The normal distribution is often used to describe and approximate any variable that tends to cluster around the mean. For example, the heights of male students in a college, the leaf sizes on a tree, the scores of a testing, etc. Use the probability of normal distribution calculator above if you want to know the possibility of a normal distribution event that will have end value between two certain numbers, for example the possibility of the height of a male student between 5 and 6 feet in a college.

In statistics, confidence interval is a way of estimating a population parameter, which provides an interval of the parameter instead of a single value. A confidence interval is always qualified by a particular confidence level, usually expressed as a percentage such as 95%. It is an indicator of the reliability of the estimate.

Probability of Two Events

In mathematics, the probability of an event A is represented by a number ranged from 0 to 1 and written to be P(A). Probability 0 means the event is not possible and probability 1 means the event is certain. The following are the basic rules for the probability of two events: