Work out complementary probability instantly with clear inputs, formula shown and shareable results.
The complement rule says P(not A) = 1 − P(A). Over independent trials the chance of no occurrence is qⁿ, so the chance of at least one is 1 − qⁿ — usually far easier than summing the cases directly.
Complement rule
P(not A) = 1 − P(A)
At least once
P(at least one in n trials) = 1 − (1 − p)ⁿ
The complement is 65%, so it never happens with probability 0.65⁵ ≈ 0.1160 and happens at least once with probability 0.8840.
Computing 'at least one' directly means summing many cases; one minus 'none' is a single calculation.