Three calculators for everyday probability questions: combine two independent events, find the chance of an event over repeated tries, and get the odds of rolling a particular total with dice.
For two independent events, the chance of both is P(A) × P(B), and the chance of at least one is P(A) + P(B) − P(A and B). With P(A) = 50% and P(B) = 30%, both happen 15% of the time, and at least one happens 65% of the time.
For repeated tries, it’s easiest to work out the chance of never succeeding and subtract from 1: P(at least once) = 1 − (1 − p)ⁿ. A 10% chance tried 10 times gives 1 − 0.9¹⁰ ≈ 65.1%, not 100%. The chance of exactly k successes uses the binomial formula: C(n, k) × pᵏ × (1 − p)ⁿ⁻ᵏ.
Dice totals are counted exactly by combining every die face. With two six-sided dice, 7 is the most likely total at 6/36 ≈ 16.7%, while 2 and 12 are the least likely at 1/36 each.
If the events are independent, multiply them: P(A and B) = P(A) × P(B). A 50% chance and a 30% chance both happen 0.5 × 0.3 = 15% of the time.
Use 1 − (1 − p)ⁿ, where p is the chance each time and n is the number of tries. Rolling a six at least once in 4 rolls is 1 − (5/6)⁴ ≈ 51.8%.
Because the tries can fail together. Each try still has a 90% chance of failing, so all ten fail 0.9¹⁰ ≈ 34.9% of the time, leaving about 65.1% for at least one success.
Seven. There are six ways to make it (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 combinations, so it comes up about 16.7% of the time.
That one event doesn’t change the chance of the other, like two separate coin flips. Drawing cards without putting them back is not independent, and needs a different calculation.
