NumberTally Probability Calculator
Single-event probability from favorable and total outcomes, plus P(A and B) and P(A or B) for two independent events — shown as a fraction, a percentage, and odds, with a visual probability gauge. Switch to binomial mode for repeated trials (coin flips, dice, free throws): exact, at-most, and at-least probabilities with the full distribution table. Results update instantly. Free, no sign-up.
e.g. 3 even faces out of 6 on a die.
Advanced options — combine two independent events
Events must be independent (one doesn't affect the other), e.g. two coin flips.
e.g. 10 coin flips.
e.g. exactly 3 heads.
e.g. 50 for a fair coin.
Trials must be independent with the same success chance each time (coin flips, dice rolls, free throws).
How Probability Works
For equally likely outcomes, probability is just favorable ÷ total: 3 even faces on a 6-sided die gives 3/6 = 50%. Two events combine with simple rules — AND (both happen) multiplies: P(A and B) = P(A) × P(B); OR (at least one happens) adds, then subtracts the overlap: P(A or B) = P(A) + P(B) − P(A and B).
The AND rule is why streaks are rarer than they feel: five heads in a row is (1/2)^5 ≈ 3% — unlikely for any specific five flips, but inevitable if you flip long enough.
Probability, Odds, and "1 in N"
The same chance wears three outfits: 25% probability = 1-in-4 = odds of 1 to 3 against. Bookmakers quote odds (profit per stake), lotteries quote "1 in N", and statisticians quote probabilities — the converter row below shows all three so you can translate fluently.
Frequently Asked Questions
What is the probability of rolling an even number?
3/6 = 50%. Three even faces (2, 4, 6) out of six equally likely faces.
How do you calculate P(A and B)?
Multiply — but only for independent events. Two 50% coin flips: 0.5 × 0.5 = 25%.
How do you calculate P(A or B)?
Add the probabilities, then subtract P(A and B) so the overlap isn't double-counted: 50% + 50% − 25% = 75%.
What is the difference between probability and odds?
Probability = favorable ÷ total. Odds against = unfavorable : favorable. 25% probability is "1 in 4" or "3 to 1 against".
What does independent mean?
One event doesn't change the other's chances — coin flips are independent, but drawing cards without replacement is not.
What is a binomial probability?
The chance of exactly k successes in n independent trials: P(X=k) = C(n,k)·p^k·(1−p)^(n−k). Use the binomial mode above — it also gives at-most and at-least totals plus the full distribution.