Probability Calculator
Probability calculator
Single-event and two-event checks in one workspace.
Single event
7.6923 %
P(A) = 4 / 52 = 0.076923
Live
P-space
0 to 1
Quick examples
Decimal
P(A)0.07692308
Percent
7.692308%
Odds for
1 : 12
Expected in 100
7.692308
Complement
P(A′)0.92307692 (92.307692%)
Probability values stay between 0 and 1 (or 0% and 100%).
Formula
P(A union B) = P(A) + P(B) - P(A intersection B) P(A \cup B) = P(A) + P(B) - P(A \cap B) P(A \mid B) = \frac{P(A \cap B)}{P(B)} P(A^\prime) = 1 - P(A) Symbol legend
| Symbol | Meaning | Unit | Copy |
|---|---|---|---|
P(A) | Probability of event A | 0 to 1 | |
P(A ∩ B) | Probability that A and B both occur | 0 to 1 | |
P(A ∪ B) | Probability that A or B or both occur | 0 to 1 | |
P(A | B) | Probability of A given B | 0 to 1 |
- For equally likely outcomes, divide favorable outcomes by total outcomes.
- For two events, identify whether they are independent, mutually exclusive, or have a known overlap.
- Subtract the overlap once when calculating a union.
- For conditional probability, divide the shared overlap by the probability of the conditioning event.
Example
Worked example: two independent events
- 1 Let P(A) = 0.4 and P(B) = 0.3.
- 2 Independent intersection: P(A ∩ B) = 0.4 x 0.3 = 0.12.
- 3 Union: P(A ∪ B) = 0.4 + 0.3 - 0.12 = 0.58.
The probability that A or B or both occur is 58%.
How
- Choose Basic, Two events, Conditional, or Complement.
- Enter probabilities as decimals or percentages, or use counts and odds in Basic mode.
- For two events, state whether the events are independent, mutually exclusive, or have a known intersection.
- Read the formula, event notation, equivalent probabilities, and exact outcome partition.
Avoid
- Multiplying P(A) and P(B) when the events are not independent.
- Adding P(A) and P(B) without subtracting their overlap.
- Treating mutually exclusive events as independent.
- Entering 40 in decimal mode instead of 0.40 or switching to percent mode.
FAQ
Can probability be greater than one?
No, probability must lie between zero and one.
Can favorable outcomes be zero?
Yes, that gives probability zero.
Does this handle dependent events?
Yes. Enter a known intersection in Two events mode or use Conditional mode to calculate P(A given B) and P(B given A).
What is the difference between independent and mutually exclusive events?
Independent events do not change each other and may overlap. Mutually exclusive events cannot occur together, so their intersection is zero.
Can I enter percentages?
Yes. Two-event, conditional, and complement modes switch between decimal and percent input without changing the represented probability.
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