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Probability Calculator

Find the chance of two independent events happening together, either one, or neither, and the chance over repeated tries.

Results

ItemValue
These results assume the events are independent, so one does not affect the other.

Quick Answer

For two independent events, multiply to find both happening: P(A and B) = P(A) × P(B). To find at least one, use P(A) + P(B) − P(A and B). With 50% and 25%, both happen 12.5% of the time, and at least one happens 62.5% of the time.

Last updated: 2 November 2026 ·How we calculate this: independent event probability rules

How This Probability Calculator Works

Probability is the chance of something happening, from 0% to 100%. Enter the chance of two independent events. The calculator shows the chance of both, either, exactly one, or neither, and the chance of A over repeated tries.

Quick explanation: independent means one event does not change the chance of the other.

  • And: multiply the probabilities.
  • Or: add them, then take away the overlap.
  • Not: subtract from 100%.

How to Use the Probability Calculator

  1. Enter the chance of event A as a percentage.
  2. Enter the chance of event B as a percentage. The events must be independent.
  3. Enter how many times event A is tried, for the repeated-tries result.
  4. Press Calculate.
  5. Read the chance of both, either, exactly one, or neither, and the chance of A at least once.

Core Formulas

  • And: P(A and B) = P(A) × P(B)
  • Or: P(A or B) = P(A) + P(B) − P(A) × P(B)
  • Not: P(not A) = 1 − P(A)
  • At least once in n tries: 1 − (1 − P(A)) ^ n

Key Terms

  • Probability: the chance of an event, from 0 (impossible) to 1, or 0% to 100%.
  • Event: an outcome or set of outcomes, such as rolling a six.
  • Independent events: events where one does not affect the other.
  • Complement: the event not happening. P(not A) = 1 − P(A).
  • Union: A or B or both happening.
  • Intersection: A and B both happening.

Worked Example

What is the chance of rolling at least one six in 4 rolls of a die?

  • Chance of a six = 1 ÷ 6, or 16.67%
  • Chance of no six in 4 rolls = (5 ÷ 6) ^ 4 = 48.23%
  • At least one six = 100% − 48.23% = 51.77%

Real-Life Examples

  • Weekend weather: if rain is 40% likely on Saturday and 30% on Sunday, treated as independent, the chance of rain on at least one day is 1 − 0.6 × 0.7 = 58%.
  • Quality checks: if 2% of items are faulty, the chance of at least one fault in 10 items is 1 − 0.98¹⁰ = 18.29%.
  • Coin flips: the chance of two heads in a row is 50% × 50% = 25%.
  • Games: a 1 in 20 chance (5%) per turn gives about 64.2% chance of at least one success in 20 turns, not 100%.

Independent vs Dependent Events

  • Independent: one result does not change the other, such as two dice or two coin flips. Multiply the chances.
  • Dependent: one result changes the next, such as drawing cards without putting them back.
  • Dependent example: the chance of two aces from a deck is 4/52 × 3/51, about 0.45%.
  • This calculator: assumes independent events.

Chance of At Least One Success

Assumes each try is independent.

Chance per try5 tries10 tries20 tries50 tries
1%4.90%9.56%18.21%39.50%
2%9.61%18.29%33.24%63.58%
5%22.62%40.13%64.15%92.31%
10%40.95%65.13%87.84%99.48%
25%76.27%94.37%99.68%100.00%
50%96.88%99.90%100.00%100.00%

Common Mistakes

  • Adding when you should multiply: use multiply for and.
  • Counting the overlap twice: subtract it for or.
  • Assuming independence: drawing cards without replacement changes the odds.
  • Past results: earlier coin flips do not change the next flip.

Frequently Asked Questions

Divide the number of favorable outcomes by the total number of possible outcomes.

If they are independent, multiply their probabilities.

It means one event does not affect the chance of the other, such as two separate coin flips.

Find the chance of no success at all, then subtract it from 100%.

Not directly. Those events are dependent, so the chance changes after each card.

On a fair six-sided die, it is 1 in 6, about 16.67%.

Odds compare chances for and against. A 25% chance is odds of 1 to 3.

For odds of 1 to 4, add the parts to get 5, so the chance is 1 ÷ 5 = 20%.

Multiply 50% three times: 0.5 × 0.5 × 0.5 = 12.5%.

Probability compares favorable outcomes with all outcomes. Odds compare favorable outcomes with unfavorable ones.

No. Probabilities run from 0% to 100%. If your answer is higher, check whether you added chances that overlap.

It is the mistaken belief that past results change the chance of an independent event. After five tails, the next flip is still 50% heads.

Each try can fail. The chance of at least one success in 10 tries at 10% is about 65.13%.

References & Sources

SourceUsed ForLink
Wikipedia, Probability Basic probability rules. https://en.wikipedia.org/wiki/Probability
Wikipedia, Independence (probability theory) Meaning of independent events. https://en.wikipedia.org/wiki/Independence_(probability_theory)