Probability Calculator
Given the probability of two independent events, this returns the three numbers that come up in every introductory probability problem: both happening, either happening, and neither happening.
Inputs
Result
P(A and B) = 0.15
P(A or B) = 0.65 · P(not A) = 0.5
How the probability calculator works
For independent events A and B: P(A and B) = P(A) × P(B).
P(A or B) = P(A) + P(B) − P(A and B) — the subtraction avoids double-counting the overlap where both occur.
P(not A) = 1 − P(A), the complement rule.
Worked example: P(A) = 0.5, P(B) = 0.3
- P(A and B) = 0.5 × 0.3 = 0.15.
- P(A or B) = 0.5 + 0.3 − 0.15 = 0.65.
- P(not A) = 1 − 0.5 = 0.5.
Common mistakes to avoid
Assuming this works for dependent events
P(A and B) = P(A) × P(B) is only valid when the two events don't influence each other. For dependent events (like drawing cards without replacement), the true joint probability requires conditional probability instead.
Forgetting to subtract the overlap in 'or' calculations
Simply adding P(A) + P(B) double-counts the outcomes where both occur — the subtraction of P(A and B) is what makes the 'or' probability correct.
Frequently asked questions
What does 'independent events' actually mean?
The outcome of one event has no effect on the probability of the other — like two separate coin flips, where the first result tells you nothing about the second.
How would this calculation change for dependent events?
You'd need the conditional probability P(B|A) — the probability of B given A has already happened — in place of the plain P(B) in the joint-probability formula.
Can probabilities entered here be percentages instead of decimals?
Enter them as decimals between 0 and 1 (0.5 for 50%) — the tool doesn't auto-convert percentage-style inputs like 50.
What's the difference between this and the Binomial Probability Calculator?
This handles two single events combined once; the binomial tool handles a fixed number of repeated independent trials, like the chance of exactly 4 heads in 10 coin flips.
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