BYTETOOLS

Probability Calculator

Work out probabilities for one or two events: complement, union, intersection, conditional probability and the chance of at least one success in n trials.

Single event

0.5 (50%)
P(A)
0.5 (50%)
P(not A)
1 : 1
Odds in favour
1 : 1
Odds against

What is the Probability Calculator?

The ByteTools Probability Calculator handles the standard single- and two-event probability questions.

  • Complement, odds for and odds against a single event
  • Union, intersection and conditional probability for two events
  • Independence toggle or custom joint probability
  • At-least-one probability across n repeated trials
  • Validates inputs against the axioms of probability
  • 100% private — computed entirely in your browser

How to use the Probability Calculator

  1. 1

    Pick a mode: single event, two events, or repeated trials.

  2. 2

    Enter the probabilities as decimals (0.25) or percentages (25%).

  3. 3

    For two events, tick 'independent' or enter the joint probability P(A and B).

  4. 4

    Read the complement, union, intersection and conditional results.

  5. 5

    Copy the summary with one click.

About the Probability Calculator

The ByteTools Probability Calculator handles the standard single- and two-event probability questions. For one event it gives the complement P(not A) and the odds for and against. For two events it computes the intersection P(A and B), the union P(A or B) via the addition rule, and the conditional probabilities P(A|B) and P(B|A).

You can treat the two events as independent — where P(A and B) = P(A) × P(B) — or supply your own joint probability for dependent events; the tool validates that your inputs are actually consistent with the axioms of probability. A repeated-trials mode answers the classic 'what is the chance of at least one success in n tries?' with 1 − (1 − p)ⁿ.

Probabilities can be entered as decimals or percentages. All calculation happens 100% locally in your browser — nothing is uploaded — making it a quick companion for homework, games of chance and risk estimates.

Frequently asked questions

How do you calculate the probability of A or B?

Use the addition rule: P(A or B) = P(A) + P(B) − P(A and B). Subtracting the intersection stops the overlap being counted twice. If the events cannot happen together (mutually exclusive), P(A and B) = 0 and you simply add.

What does it mean for two events to be independent?

Events are independent when one occurring tells you nothing about the other, so P(A and B) = P(A) × P(B). Coin flips are independent; drawing cards without replacement is not. This calculator lets you toggle independence or enter the joint probability directly.

How do you calculate the probability of at least one success?

Take the complement of zero successes: P(at least one) = 1 − (1 − p)ⁿ. With a 10% chance per trial and 10 trials, that is 1 − 0.9¹⁰ ≈ 65.1%. It rises quickly with n but never reaches 100%.

What is conditional probability?

P(A|B) is the probability of A given that B has occurred, computed as P(A and B) / P(B). It rescales the probability to the world where B is known to be true, and it is the foundation of Bayes' theorem.

What is the difference between probability and odds?

Probability is successes over all outcomes; odds compare successes to failures. A probability of 0.25 equals odds of 1:3 in favour (one success for every three failures). This tool reports both formats for single events.

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