What is the fundamental formula for probability?

The probability of an event is `P(E) = Number of Favorable Outcomes / Total Possible Outcomes`. Probabilities always range between 0 (impossible) and 1 (certain).

What is the difference between mutually exclusive and independent events?

Mutually exclusive events cannot happen at the same time (`P(A and B) = 0`). Independent events can happen together, and the occurrence of one does not affect the probability of the other.

What is the complement rule in probability?

The complement of event A is the event that A does not happen: `P(not A) = 1 - P(A)`.

How do you calculate conditional probability P(A|B)?

Conditional probability is the probability of event A occurring given that B has already occurred: `P(A|B) = P(A and B) / P(B)`.

How do you convert probability to odds?

Odds in favor of an event are calculated as `Odds = P(A) / [1 - P(A)]`. For example, a 25% probability equals odds of `0.25 / 0.75 = 1 to 3`.

How do I calculate the joint probability of two independent events both occurring?

Multiply the individual probabilities together: `P(A and B) = P(A) × P(B)`. For example, rolling two sixes on dice is `(1/6) × (1/6) = 1/36`.

Math & Statistics Cluster

Probability Calculator (Single, Union & Joint Events)

Calculate event probabilities, unions $P(A \cup B)$, intersections $P(A \cap B)$, and conditional rules.

TL;DR: Probability Calculator computes the probability of single and multiple events, calculating intersections $P(A \text{ and } B)$, unions $P(A \text{ or } B)$, and complements.

P(A) %

P(B) %

Assumes A and B are independent events (one doesn't affect the other).

How Do You Calculate the Probability of Two Events Occurring Together?

For two independent events A and B, the probability of both occurring is: P(A and B) = P(A) × P(B). The probability of either event occurring is: P(A or B) = P(A) + P(B) - P(A and B).

How to Use the Probability Calculator

Our Probability Calculator performs high-precision mathematical operations directly in your browser with zero latency and complete client-side privacy.

Select your probability calculation type: Single Event, Two Events (A and B), or Series of Trials.
Enter probability values as decimals (0 to 1), percentages (0% to 100%), or ratios (1 in X).
Specify whether events are Independent, Dependent, or Mutually Exclusive.
Click 'Calculate Probability' to view union, intersection, and complement results.
Review odds ratios and visual Venn diagram representations.

Mathematical Formula & Equations

Computes single event, independent compound event, mutually exclusive, and conditional Bayes probabilities.

\[ P(A) = \frac{n(A)}{n(S)}, \quad P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

Calculation Example

Probability of rolling a sum of 7 with two six-sided dice: 6 favorable outcomes out of 36 total possibilities $P = \frac{6}{36} = \frac{1}{6} \approx 16.67\%$.

100% Client-Side Privacy & Data Security

All calculations, amortization schedules, variables, and sensitive numerical datasets execute 100% locally in your web browser memory. Your financial, medical, and personal values are never transmitted, logged, or uploaded to any external server.

Frequently Asked Questions

: The probability of an event is `P(E) = Number of Favorable Outcomes / Total Possible Outcomes`. Probabilities always range between 0 (impossible) and 1 (certain).
: Mutually exclusive events cannot happen at the same time (`P(A and B) = 0`). Independent events can happen together, and the occurrence of one does not affect the probability of the other.
: The complement of event A is the event that A does not happen: `P(not A) = 1 - P(A)`.
: Conditional probability is the probability of event A occurring given that B has already occurred: `P(A|B) = P(A and B) / P(B)`.
: Odds in favor of an event are calculated as `Odds = P(A) / [1 - P(A)]`. For example, a 25% probability equals odds of `0.25 / 0.75 = 1 to 3`.
: Multiply the individual probabilities together: `P(A and B) = P(A) × P(B)`. For example, rolling two sixes on dice is `(1/6) × (1/6) = 1/36`.

Cite This Calculator

Need to reference this online calculator in a financial proposal, academic paper, blog post, or classroom curriculum? Copy a citation below.

NexLove.org. (2026). Probability Calculator [Online Calculation Tool]. https://nexlove.org/tools/probability-calculator

“Probability Calculator.” NexLove.org, 2026, nexlove.org/tools/probability-calculator.

NexLove.org (2026) Probability Calculator. Available at: https://nexlove.org/tools/probability-calculator (Accessed: 2026).

@misc{nexlove_probability_calculator,
  title = {Probability Calculator},
  author = {{NexLove.org}},
  year = {2026},
  url = {https://nexlove.org/tools/probability-calculator}
}

Embed This Tool

Add the live Probability Calculator to your own website with this snippet — it loads the real, working calculator in an iframe.

<iframe src="https://nexlove.org/embed/probability-calculator.html" width="100%" height="600" style="border:1px solid #e2e8f0;border-radius:12px" title="Probability Calculator — NexLove.org" loading="lazy"></iframe>

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