Combinatorial Probability Calculator

How it is calculated

The tool applies classical probability: P = f / t, where f is the number of favorable outcomes and t the total number of equally likely outcomes. The percentage is P × 100. The odds are shown as odds against: (t − f) / f : 1, meaning how many unfavorable outcomes there are for each favorable one. Both counts are whole numbers; any decimals you type are cut off (2.9 is read as 2). The result is empty if the total is zero, if the favorable count is negative, or if it is larger than the total. With zero favorable outcomes the odds read "never". The formula is only valid when every outcome is equally likely.

Common mistakes

• Reading the odds as favorable : unfavorable. The tool gives odds against (unfavorable per one favorable), so 12.00 : 1 means 12 misses for each hit, not the other way around.
• Using total outcomes that are not equally likely, such as the sum of two dice (7 is more likely than 2). Count the 36 ordered rolls, not the 11 possible sums.
• Entering the probability as a percentage or fraction instead of counts. The fields expect whole numbers of outcomes.
• Typing a decimal count such as 2.5, which is silently cut to 2 and changes the result.
• Forgetting that order matters or does not matter when you work out the counts with permutations or combinations first, so the favorable and total counts are not counted the same way.