Calculators
Probability Calculator
Calculate basic, combined, conditional, and complement probabilities.
Probability Calculator tool
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About This Tool
Probability measures how likely an event is, from 0 for impossible to 1 for certain. This calculator brings several common introductory probability tasks into one page: favorable outcomes out of equally likely total outcomes, the intersection or union of independent events, conditional probability from an intersection, and the complement of every calculated result. Each mode states the assumption it relies on so similar-looking formulas are not applied to the wrong situation.
How To Use It
- Choose Favorable / total outcomes when every outcome in the sample space is equally likely, then enter whole-number counts no greater than 9,007,199,254,740,991, the browser's exact integer limit.
- Choose A and B or A or B only when events A and B are independent. Enter probabilities in decimal form between 0 and 1, such as 0.25 for 25%.
- Choose Conditional P(A|B) when you know P(B) and P(A and B). The result is the probability of A given that B occurred.
- Read the result as both a percentage and decimal. The complement shows the probability that the calculated event does not occur.
Examples
Rolling one specific number
A fair six-sided die has 1 favorable outcome among 6 equally likely outcomes. The probability is 1/6 ≈ 0.1667, or about 16.67%.
Two independent events both occur
If P(A) = 0.5 and P(B) = 0.4 and the events are independent, P(A and B) = 0.5 × 0.4 = 0.2, or 20%.
At least one independent event occurs
For independent events with probabilities 0.5 and 0.4, P(A or B) = 0.5 + 0.4 − (0.5 × 0.4) = 0.7, or 70%.
Conditional probability
If P(B) = 0.5 and P(A and B) = 0.2, then P(A|B) = 0.2 / 0.5 = 0.4, or 40%.
Useful Notes
Probability from equally likely outcomes
When outcomes are equally likely, P(A) = favorable outcomes / total outcomes. This shortcut is not appropriate when outcomes have different chances, because simply counting them would ignore their unequal weights.
Independent AND probability
For independent events, P(A and B) = P(A) × P(B). Independence means learning whether one event occurred does not change the probability of the other. If events are dependent, this multiplication rule needs conditional probability instead.
Independent OR probability
For two independent events, P(A or B) = P(A) + P(B) − P(A)P(B). The intersection is subtracted because adding P(A) and P(B) counts outcomes where both happen twice.
Conditional probability
Conditional probability is P(A|B) = P(A and B) / P(B), provided P(B) is greater than zero. The intersection cannot be larger than P(B), so the calculator rejects inconsistent inputs.
Complements
The complement rule is P(not A) = 1 − P(A). It is often easier to calculate the chance that an event does not happen and subtract it from 1, especially in 'at least one' problems with repeated independent trials.
Decimals, percentages, and assumptions
The event modes accept decimal probabilities from 0 through 1. For example, enter 0.35 for 35%. Results are mathematical probabilities based only on the values and assumptions supplied; they do not estimate real-world chances without an appropriate probability model.
FAQ
What is the difference between AND and OR probability?
AND asks for the chance that both events occur. OR asks for the chance that at least one occurs. Their formulas differ because overlapping outcomes must be handled correctly.
When can I use the independent-event modes?
Use them only when one event occurring does not change the probability of the other. Drawing a card and replacing it before a second draw can be independent; drawing without replacement generally is not.
Why must P(B) be greater than zero for P(A|B)?
Conditional probability divides P(A and B) by P(B). Conditioning on an event with probability zero makes that formula undefined.
Can favorable outcomes be greater than total outcomes?
No. In an equally likely sample space, favorable outcomes are a subset of all possible outcomes, so their count cannot exceed the total.