Statistical Logic Suite

Probability Calculator

Calculate the likelihood of events, solve for unknown parameters, and explore distributions with industrial precision.

Probability of Two Events

Analyze basic relationships between two independent events A and B.

Probability of A - P(A)0 to 1

Probability of B - P(B)0 to 1

Enter P(A) and P(B) to analyze relationships

Probability Solver

Enter any TWO values to solve for the remaining six parameters (assuming independence).

P(A)

P(B)

P(A ∩ B)

P(A ∪ B)

P(A Δ B)

P((A ∪ B)')

Independent Series Analyzer

Calculate outcome likelihoods across multiple trials of event A and B.

Prob. of A

A Trials (n)

Prob. of B

B Trials (m)

Analyze outcome combinations across multiple events

Normal Distribution

Calculate area (probability) under the Gaussian bell curve.

Mean (μ)

Std Dev (σ)

Lower Bound (L)

Upper Bound (R)

Awaiting Distribution Parameters

Theory

The Math of
Likelihood

Probability is a mathematical measure of the likelihood that an event will occur. It is quantified as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

Complement Rule

The probability of an event not occurring is simply 1 minus the probability that it does.
P(A') = 1 - P(A)

Independence

Two events are independent if the occurrence of one does not affect the probability of the other.
P(A ∩ B) = P(A) × P(B)

Visualizing Event Logic

Intersection (AND)

The overlapping region where both A and B occur.

Union (OR)

The total area covering either A, B, or both.

Symmetric Diff (XOR)

Region where exactly one event occurs, but not both.

The Normal Distribution

Often called the Gaussian distribution, it describes how data points are distributed around a mean. Its symmetrical "bell shape" is foundational to statistics, appearing in natural phenomena from human height to standardized test scores.

Empirical Rule (68-95-99.7)

68%

Within 1 σ

95%

Within 2 σ

99.7%

Within 3 σ

Standard Normal (Z) Table

Showing P(Z ≤ z) for z ≥ 0

z	.00	.01	.02	.03	.04	.05	.06	.07	.08	.09
0.0	0.5000	0.5040	0.5080	0.5120	0.5160	0.5200	0.5239	0.5279	0.5319	0.5359
0.5	0.6916	0.6951	0.6986	0.7021	0.7055	0.7090	0.7124	0.7158	0.7192	0.7225
1.0	0.8413	0.8437	0.8461	0.8485	0.8508	0.8531	0.8554	0.8576	0.8599	0.8621
1.5	0.9331	0.9343	0.9356	0.9369	0.9381	0.9393	0.9405	0.9417	0.9428	0.9439
2.0	0.9772	0.9778	0.9783	0.9788	0.9793	0.9798	0.9803	0.9808	0.9813	0.9817
2.5	0.9939	0.9941	0.9943	0.9944	0.9946	0.9947	0.9949	0.9951	0.9952	0.9953
3.0	0.9988	0.9988	0.9989	0.9989	0.9989	0.9990	0.9990	0.9990	0.9991	0.9991

Table values represent the area under the standard normal curve to the left of Z.

Explore Advanced Statistics

Need to analyze your dataset before calculating probabilities? Use our Standard Deviation Calculator for a deep dive into your data's variance.

How the calculation works

Probability of one equally likely outcome is 1 divided by the number of outcomes. Independent events multiply.

P(A and B) = P(A) × P(B) when the events are independent

A fair die has 6 faces. Two independent dice have 36 outcomes.

Worked example: two fair dice

P(a six on one die) = 1/6.
P(two sixes) = 1/6 × 1/6 = 1/36.
P(at least one six) = 1 − (5/6)² = 11/36.

One fair die

Event	Probability
Any one face	1/6
Even number	1/2
Two sixes on two dice	1/36

Frequently asked questions

What is the chance of two sixes on two fair dice?▼

1/36.

What is the chance of at least one six?▼

11/36.

When do you add probabilities instead?▼

For mutually exclusive events. You cannot roll a 2 and a 3 on one die at the same time, so those probabilities add.