This probability calculator works out the chances of single events and of two events combined — both happening, either happening, or one but not the other. It also includes a quick dice tool for the probability of any total with two dice.
Single Event
Two Independent Events
What Is Probability?
Probability is the measure of how likely something is to happen, written as a number between 0 (impossible) and 1 (certain) — or as a percentage. The basic formula is:
P(event) = favorable outcomes ÷ total possible outcomes
Rolling a 4 on one die: 1 favorable outcome out of 6, so 16.67%. Drawing an ace from a full deck: 4 out of 52, so 7.69%. This calculator covers those single events and the combinations students and analysts need most. It belongs to our Statistics Calculators collection.
Probability of Two Events (Formulas)
- Both happen — P(A and B) = P(A) × P(B) for independent events. Two coin heads in a row: 0.5 × 0.5 = 25%.
- At least one happens — P(A or B) = P(A) + P(B) − P(A and B). At least one head in two flips: 50 + 50 − 25 = 75%.
- Neither happens = (1 − P(A)) × (1 − P(B)). No heads in two flips: 25%.
- Exactly one happens = P(A or B) − P(A and B).
“Independent” means one event does not change the other’s odds — coin flips and dice rolls qualify; drawing cards without replacing them does not, because the deck changes.
Dice Probabilities
With two dice there are 36 equally likely combinations, and the totals are not equally likely: 7 is the most common total (6 ways, 16.67%), while 2 and 12 are the rarest (1 way each, 2.78%). The calculator prints the full table for every total — the pattern behind many board-game and craps decisions. For a playful test of probability intuition, try our Monty Hall Simulator — the famous problem where switching doors doubles your win chance from 33.3% to 66.7%.
Probability vs. Odds
Probability compares favorable outcomes with all outcomes (1/6 for rolling a 4). Odds compare favorable with unfavorable (1:5 for the same roll). Bookmakers quote odds; statistics uses probability. The calculator shows both for your single event. For data-distribution probabilities instead of event counting, use the Z-Score Calculator, and for spread of measured data, the Standard Deviation Calculator.
Related Tools
- Standard Deviation Calculator — spread of a data set, with steps
- Z-Score Calculator — probabilities under the normal curve
- Monty Hall Simulator — the classic probability puzzle
Frequently Asked Questions
How do I calculate the probability of multiple events?
For independent events both happening, multiply the individual probabilities. For at least one happening, add them and subtract the overlap (the “and” probability) — the formulas above, done automatically by this calculator.
What is the probability of rolling a 7 with two dice?
6 out of 36 combinations total 7, so 16.67% — the single most likely total.
Can probability be more than 100%?
No. Probability runs from 0% (impossible) to 100% (certain). If your calculation exceeds 100%, you have probably added overlapping events without subtracting the overlap.
What are dependent events?
Events where one outcome changes the other’s odds — like drawing a second card without replacing the first. The simple multiply rule needs adjustment (conditional probability) for those.
How do I convert odds to probability?
For odds of a:b in favor, probability = a ÷ (a + b). Odds of 1:5 → 1/6 → 16.67%.
Is this probability calculator free?
Yes — free, instant, no sign-up.