Probability Calculator · Practical guide
Probability That an Event Does Not Occur
The complement rule: the chance something does not happen is 1 minus the chance it does.
At a glance
The Complement Rule
Every event either happens or it does not, so the two probabilities must total 1. The probability that an event does not occur is P(A') = 1 − P(A). A 25% chance of rain means a 75% chance of staying dry.
Interactive tool
Probability Calculator
Enter your own values, then compare the result with the examples below.
Worked Examples
| Event Probability P(A) | Complement P(A') = 1 − P(A) | As a Percentage |
|---|---|---|
| 0.6 | 0.4 | 40% |
| 0.25 | 0.75 | 75% |
| 0.95 | 0.05 | 5% |
| 0.01 | 0.99 | 99% |
When the Complement Is the Easy Path
"At least once" problems are much simpler in reverse. The chance of at least one heads in 3 coin flips equals 1 minus the chance of no heads at all: 1 − 0.5³ = 1 − 0.125 = 0.875, an 87.5% chance. Computing it directly would mean adding up several overlapping cases.
Entering Percentages
The calculator accepts decimals between 0 and 1 — but if you type 25 instead of 0.25, it treats the value as a percentage and divides by 100 automatically. Either way, the Single Event tab returns P(A) and its complement side by side.
Frequently Asked Questions
What is the complement of a certain event?
Zero. If P(A) = 1, then P(A') = 1 − 1 = 0 — something guaranteed to happen has no chance of not happening.
Do P(A) and P(A') always add up to 1?
Yes, by definition. An event and its complement cover every possible outcome with no overlap, so their probabilities must total exactly 1.
What is the probability of no heads in 4 coin flips?
Each flip misses heads with probability 0.5, and the flips are independent: 0.5^4 = 0.0625, a 6.25% chance.
Is the complement the same as the opposite event?
Yes. Complement is the technical term for "everything except A" — all outcomes where the event fails to occur.