Probability Calculator for Independent Events
Enter the chance of event A (and event B for two events) as percentages, pick what you want to find and read the result.
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Formula
Write each probability as a decimal (30% is 0.3). For independent events A and B:
P(A) = P(A)(single event)P(not A) = 1 − P(A)(complement)P(A and B) = P(A) × P(B)P(A or B) = P(A) + P(B) − P(A) × P(B)P(neither) = (1 − P(A)) × (1 − P(B))
Worked example
Event A has a 30% chance and event B has a 40% chance, and they are independent:
- Both happen: 0.3 × 0.4 = 0.12 (12%)
- At least one happens: 0.3 + 0.4 − 0.12 = 0.58 (58%)
- Neither happens: 0.7 × 0.6 = 0.42 (42%)
- A does not happen: 1 − 0.3 = 0.7 (70%)
Frequently asked questions
How do I find the probability of two independent events both happening?
Multiply the two probabilities. If A is 30% (0.3) and B is 40% (0.4), both happen with probability 0.3 × 0.4 = 0.12, which is 12%.
How do I find the probability that A or B happens?
Add the probabilities and subtract the chance of both, so the overlap is not counted twice: 0.3 + 0.4 − 0.12 = 0.58, or 58%.
What is the complement of an event?
The complement is the chance the event does not happen: 100% minus its probability. If it rains with 30% probability, it stays dry with 70% probability.
When can I treat two events as independent?
Events are independent when one happening does not change the chance of the other, such as two coin flips. Drawing cards without putting them back is not independent, so these formulas do not apply.