Probability Calculator — Events, At Least One, Dice and Lottery Odds

This probability calculator covers the questions people actually ask: the chance that two events both happen, either happens or neither does; the chance of getting at least one success in a number of tries (a 1% drop rate, a gacha pull, a free throw); the odds of rolling a given total with several dice; and the odds of winning a lottery jackpot.

How to use this tool

1. Pick a mode: two events, repeated tries, dice sums or lottery odds.
2. Enter the probabilities as percentages (50 for 50%), or the dice and lottery details.
3. For two events, say whether they are independent, mutually exclusive or give P(A and B).
4. Read the results; the table shows the full distribution or the number of tries you need.

Formula

P(A or B) = P(A) + P(B) − P(A and B) · P(at least one in n) = 1 − (1 − p)^n · P(exactly k) = C(n, k) p^k (1 − p)^(n − k)

For independent events P(A and B) = P(A) × P(B); conditional probability P(A | B) = P(A and B) ÷ P(B). Tries needed for a chance q are ⌈ln(1 − q) ÷ ln(1 − p)⌉. Dice sums come from convolving one die's distribution with itself. Lottery odds are C(N, k), the number of ways to choose k numbers from N, times the bonus pool size if there is one.

Example

With a 1% drop rate, 100 tries give a 1 − 0.99¹⁰⁰ = 63.4% chance of at least one drop — not 100%. You need 69 tries for a 50% chance and 230 for 90%. With two six-sided dice, a total of 7 comes up 6 ways out of 36, 16.67% of rolls.