Probability Calculator - Single & Combined Events
Calculate probability for a single event, two independent events both happening, or at least one of two events happening.
Probability
0.1667
16.67%
How to Calculate Probability
This calculator covers three common probability scenarios. A single event's probability is favorable outcomes divided by total possible outcomes. For two independent events (where one doesn't affect the other), the probability that both happen is found by multiplying their individual probabilities. The probability that at least one of two independent events happens is 1 minus the probability that neither happens.
Example
Rolling a 6-sided die and wanting a specific number gives P = 1 ÷ 6 ≈ 0.167. If you flip a coin (P = 0.5) and roll a die and want heads (P = 0.5), the probability both happen is 0.5 × 0.5 = 0.25. The probability of getting heads OR rolling that number is 1 − (1 − 0.5)(1 − 0.167) ≈ 0.583.
Common Use Cases
- Calculating odds for dice games, card draws, or lottery-style probability questions.
- Combining the probability of two independent events for statistics coursework.
- Estimating the chance that at least one of several independent risks or events occurs.
FAQs
What does "independent events" mean?
Two events are independent if the outcome of one has no effect on the outcome of the other, like flipping a coin twice or rolling two separate dice. The multiplication and "at least one" formulas here only apply to independent events — dependent events require conditional probability instead.
Why isn't P(A or B) just P(A) + P(B)?
Simply adding the probabilities would double-count the case where both events happen. The formula 1 − (1 − P(A))(1 − P(B)) correctly accounts for this by first finding the probability that neither event happens, then subtracting that from 1.
Can probability be greater than 1 or less than 0?
No — probability is always between 0 (impossible) and 1 (certain), inclusive. This calculator expects inputs within that valid range for the compound event modes.