Updated · Built and checked by the PlinzoTools team, formulas tested against published sources
Calculate the probability of a single event and its complement.
This tool calculates the probability of a simple event -- the chance of a specific outcome occurring, given the number of favorable outcomes and total possible outcomes.
Enter the number of favorable outcomes and the total number of possible outcomes. Probability and its complement (the chance of the event NOT happening) appear instantly.
P(event) = favorable outcomes / total outcomes
P(not event) = 1 - P(event)
The hardest part of a probability question is usually deciding what to type into the two boxes. The tool only divides one count by another, so the quality of the answer depends entirely on counting correctly. Enter the number of outcomes that count as success, then the total number of possible outcomes, and make sure every outcome in the total is equally likely.
Here are two hypothetical examples with different counts.
Drawing a heart from a standard 52-card deck: 13 favorable of 52 total = 0.25, or 25%. The complement is 75%.
Rolling two six-sided dice and getting a sum of 7: 6 favorable of 36 total ≈ 16.67%. The complement is about 83.33%.
The second example shows why the total should list every combined outcome. Two dice have 6 × 6 = 36 equally likely pairs, and six of them add up to 7: 1+6, 2+5, 3+4, 4+3, 5+2, and 6+1. Using 11 for the total, the number of possible sums, would be wrong because the sums are not equally likely.
The total must be greater than zero, and the favorable count must be between 0 and the total. Otherwise the tool shows a message instead of a result, since a probability cannot be negative or exceed 100 percent. A favorable count of 0 gives 0 percent (impossible) and a favorable count equal to the total gives 100 percent (certain). The result is shown as a percentage to two decimal places, and the complement is displayed the same way.
The complement, the chance that the event does not happen, is often easier to reason about. A classic use is "at least one" questions. To find the chance of getting at least one head in two coin flips, count the single outcome with no heads (tails, tails), which has probability 1/4, and subtract from 1 to get 3/4, or 75 percent. You would calculate the "none" case with a compound-event step by hand, since this tool handles just one simple event, and then use the complement figure to finish.
You can use this calculator to get each single-event probability, then combine them with those rules.
No -- this calculates a single simple event's probability. For compound events, multiply/add individual probabilities according to whether they're independent, mutually exclusive, etc.
Probability is favorable outcomes divided by total outcomes. Odds compare favorable to unfavorable outcomes. A 25 percent probability corresponds to odds of 1 to 3.
The total must be greater than 0 and the favorable count must be between 0 and the total. Anything outside that range cannot be a valid probability.
Not directly. The method assumes each outcome is equally likely. For weighted outcomes, you need to work with the individual probabilities yourself.
Calculate the probability that no success happens across all trials, then subtract that from 1. The complement figure this tool shows helps with the single-event step.
Reference: NIST Weights and Measures