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Probability Calculator

Combine the chances of two independent events, and of one happening at least once in many tries.

By Nitin Raturi · Last reviewed

Your events

How to use the Probability Calculator

Combine the chances of two independent events.

  1. Enter the chance of A and the chance of B as percentages.
  2. Enter how many times A is tried.
  3. Read the chance of both, either, neither and exactly one.
  4. Read the chance A happens at least once in all the tries.

Good to know

  • Convert a fraction to a percentage first: 1 in 6 is 16.67%.
  • For dependent events these formulas do not apply.

Chance of A

How likely the first event is, as a percentage.

How to fill it in

  • Enter 0% to 100%. A fair coin landing heads is 50%.

Example

Heads and a 6 on one die together: 8.33%.

Chance of B

How likely the second event is. It must not depend on A.

How to fill it in

  • Enter 0% to 100%. One face of a die is 16.67% (1 in 6).

Example

Two dice both showing 6: 2.78%.

Keep in mind: The formulas assume A and B are independent: one happening does not change the other’s chance.

Tries of A

How many times A gets a chance, to find the chance it happens at least once.

How to fill it in

  • Enter a whole number from 1 to 10,00,000.

Example

A 1% chance tried 100 times happens at least once 63.40% of the time, not 100%.

Chance of both A and B

8.33%

Both happen 8.33% of the time, at least one 58.33%, and A happens at least once in 10 tries 99.90% of the time.

A or B (at least one)
58.33%
Exactly one
50.00%
Neither
41.67%
Not A / not B
50.00% / 83.33%
A at least once in 10 tries
99.90%
A never in 10 tries
0.10%

A and B are independent. P(A and B) = P(A) × P(B); P(A or B) = P(A) + P(B) − P(A and B).

ChangelogHow we test this calculatorEmbed this calculator

How this calculator works

  1. Step 1BothP(A) × P(B)Multiply when both must happen.
  2. Step 2EitherP(A) + P(B) − bothAdd, then remove the overlap counted twice.
  3. Step 3Repeated tries1 − (1 − p)ⁿOne minus the chance of missing every time.

Independent events do not affect each other: a coin toss tells you nothing about a die roll. Their chances combine by these simple rules.

Worked example: a coin and a die

Heads (1/2) and a six (1/6)
Both
P(A) × P(B)
Either
P(A) + P(B) − P(A) × P(B)
  1. Both1/2 × 1/6 = 1/128.33%
  2. Either1/2 + 1/6 − 1/12 = 7/1258.33%
  3. Neither1/2 × 5/6 = 5/1241.67%
  4. Heads at least once in 101 − (1/2)¹⁰99.90%

Two dice both showing a six is rarer: 2.78%, or 1 in 36.

A 1% chance, many times

  • Once1%
  • 100 tries63.40%
Chance a 1% event happens at least once

A 1-in-100 chance tried 100 times is not certain: it happens at least once only about 63% of the time.

Assumptions and limits

  • IndependentOne event does not change the other’s chance.
  • Same chance each tryEvery try of A has the same probability.
  • PercentagesEnter 1 in 6 as 16.67%.
  • Not dependent eventsDrawing cards without replacing them needs other rules.

Combining two events is the simplest probability. Counting outcomes and repeated trials have their own tools.

To count arrangements and selections, use the permutation and combination calculator. For a fixed number of tries, the binomial distribution calculator gives exact chances, and the dice roller shows every total’s odds.

Common mistakes

  • Mistake: Adding chances for “either”.

    Instead: Subtract the overlap: 50% + 50% is 75%, not 100%.

  • Mistake: Multiplying chances of dependent events.

    Instead: Use the chance of B given A.

  • Mistake: Expecting n tries at 1/n to be certain.

    Instead: It is about 63% for large n.

Checking the method

A separate script re-works every golden value from the truth table and a binomial sum, in exact fractions.

Read how we test our calculators, or browse more maths calculators.

Frequently asked questions

What is the chance of heads and a six?

8.33%: 1/2 × 1/6 = 1/12.

How do I find the chance of A or B?

Add them and subtract both: heads or a six is 58.33%.

What is the chance of two sixes?

2.78%, or 1 in 36: 1/6 × 1/6.

If something has a 1% chance, how likely is it in 100 tries?

63.40%: 1 − 0.99¹⁰⁰. Not certain.

What does independent mean?

One event happening does not change the chance of the other, like separate coin tosses.

Sources and methodology

The formulas are standard time-value-of-money results. We check every figure against golden values worked out independently, by closed form and by month-by-month simulation; see the methodology.

Written and maintained by Nitin Raturi, a software engineer (about the author). Last reviewed 4 Nov 2026; next review due by . Found an error? Tell us.

Changelog

  • : Initial release.