🎲 Probability Calculator

Calculate a single event's probability, or combine two independent events.

About this tool

Calculates basic probability as favorable outcomes divided by total possible outcomes, and separately combines two independent events using the standard AND (both happen) and OR (at least one happens) formulas.

Both calculators assume the events involved are independent — the outcome of one doesn't affect the other, as with two separate dice rolls or two unrelated coin flips.

Worked example

Rolling a 6-sided die, the probability of landing on a specific number is 1/6, about 16.67%. Two independent 50% events both happening (AND) is 25%; at least one happening (OR) is 75%.

How to use it

For a single event, enter the number of favorable outcomes and the total possible outcomes.
For combined events, enter each event's probability as a percentage and see both the AND and OR results.

Tips

"P(A and B)" for independent events is simply P(A) × P(B) — this only holds when the two events don't influence each other.
"P(A or B)" uses the formula P(A) + P(B) − P(A and B) to avoid double-counting the overlap where both happen.
This tool assumes independence; for dependent events (where one outcome changes the odds of the other), a different, conditional-probability approach is needed.

FAQ

What does "independent events" mean?

It means the outcome of one event has no effect on the probability of the other — like separate coin flips or dice rolls, as opposed to drawing cards from a deck without replacement, where each draw changes the odds for the next.

Why subtract P(A and B) in the OR formula?

Adding P(A) + P(B) directly would double-count the outcomes where both A and B happen, so subtracting the overlap once corrects for that.

Can favorable outcomes be more than half the total?

Yes, absolutely — anywhere from 0 up to the full total is valid, giving a probability anywhere from 0% to 100%.

From the blog: getting the most out of this tool

Probability is a topic where the arithmetic is simple but the setup is where mistakes creep in — mixing up AND and OR, or forgetting to subtract the overlap, are the two most common errors people make doing this by hand, and both formulas are laid out explicitly here so the reasoning stays visible, not just the answer.

We limited this to independent events deliberately — conditional probability (where events do affect each other) needs a meaningfully different formula, and folding it into the same simple tool would risk giving a confidently wrong answer to a genuinely different question.