Statistics

Probability Calculator

Combined probability of independent events.

Enter your values

Enter the probability of a in %.

Enter the probability of b in %.

Enter the repeated trials of a you are working with.

Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.

Results
Both A and B
13.5%
A or B (either)
61.5%
Neither
38.5%
A at least once in 5 trials
83.193%
Odds of A
0.429 to 1

Quick answer

For independent events, P(A and B) = P(A)·P(B) and P(A or B) = P(A) + P(B) − P(A)·P(B).

P(A∩B) = P(A)·P(B)

At a glance

What it doesCombined probability of independent events.
CategoryStatistics
Inputs neededProbability of A, Probability of B, Repeated trials of A
Main outputBoth A and B
FormulaP(A∩B) = P(A)·P(B)
CostFree — no sign-up, no download

How to use the Probability Calculator

  1. 1Enter the probability of each event as a percentage.
  2. 2Set repeated trials if you want the 'at least once' figure.
  3. 3Read the combined probabilities.

Inputs explained

Probability of A(%)
Enter the probability of a in %.
Probability of B(%)
Enter the probability of b in %.
Repeated trials of A
Enter the repeated trials of a you are working with.

Worked example

Using the values the calculator loads with:

Inputs

  • Probability of A30 %
  • Probability of B45 %
  • Repeated trials of A5

Results

  • Both A and B13.5%
  • A or B (either)61.5%
  • Neither38.5%
  • A at least once in 5 trials83.193%
  • Odds of A0.429 to 1

Frequently asked questions

What does independent mean?

One event's outcome doesn't change the other's probability. Two coin flips are independent; drawing cards without replacement is not.

Why is 'at least once' so high?

Failure has to happen every single time, and (1−p)^n shrinks fast — a 10% chance over 20 tries is 88% likely to occur.

What do I need to enter into the Probability Calculator?

Just 3 values: probability of a, probability of b, repeated trials of a. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.

How does the Probability Calculator work out the answer?

For independent events, P(A and B) = P(A)·P(B) and P(A or B) = P(A) + P(B) − P(A)·P(B). It applies the formula P(A∩B) = P(A)·P(B) and shows the working so you can check each step by hand.

Is the Probability Calculator free, and do I need an account?

It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.

Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.