Single event or two independent events.
P(E) = f / n
The probability of a single event is calculated by dividing the number of favorable outcomes (ways the event you care about can happen) by the total number of equally likely possible outcomes. The result is always a number between 0 and 1, where 0 means the event cannot happen and 1 means it is certain to happen. Multiply by 100 to convert to a percentage.
P(Red) = f / n = 26 / 52 = 0.5
Result: P(Red) = 0.5 = 50% As a fraction: 1/2
A probability of 0.5 (50%) means that, on average, you would expect to draw a red card about half the time over many repeated draws. This makes intuitive sense because exactly half the cards in a standard deck are red. A probability closer to 1 means an event is very likely; a probability closer to 0 means it is very unlikely.
Probability is a branch of mathematics that quantifies uncertainty. For a single event with equally likely outcomes, the classical definition — developed by Pierre-Simon Laplace — states that probability equals favorable outcomes divided by total outcomes.
| Probability | Meaning | |---|---| | 0 | Impossible | | 0.25 | Unlikely (25%) | | 0.5 | Even chance (50%) | | 0.75 | Likely (75%) | | 1 | Certain |
Probability can be expressed three ways:
All three are equivalent and interchangeable.
Probability underpins weather forecasting, insurance pricing, medical testing (sensitivity and specificity), quality control in manufacturing, and game design. Understanding even basic single-event probability gives you a powerful tool for making informed decisions under uncertainty.
Multiply their individual probabilities. If P(A) = 0.5 and P(B) = 0.25, then P(A and B) = 0.5 × 0.25 = 0.125 (12.5%). This is the multiplication rule for independent events.
Theoretical probability is calculated using the formula P = f/n based on known outcomes (like a fair die). Experimental probability is determined by actually running trials and recording results: P = (number of times event occurred) / (total trials). As trials increase, experimental probability tends toward theoretical probability — this is the Law of Large Numbers.
Probability is used in weather forecasts (a 70% chance of rain), medical diagnoses (a test's sensitivity and specificity), insurance premium calculations, financial risk models, and even sports analytics (win probability). Understanding single-event probability is the foundation for all these applications.
A uniform distribution means every outcome in the sample space is equally likely. Rolling a fair die or drawing a random card from a well-shuffled deck are classic examples. The simple P = f/n formula applies directly to uniform distributions.
Probability is the ratio of favorable outcomes to total outcomes (f/n). Odds compare favorable outcomes to unfavorable outcomes (f : n−f). For example, rolling a 6 on a die has a probability of 1/6 ≈ 16.67%, but odds of 1:5 (one favorable vs. five unfavorable).
No. By definition, probability must be between 0 and 1 (inclusive). A value of 0 means the event is impossible; a value of 1 means it is certain. If you get a result outside this range, check that your inputs are correct.
Simply count all outcomes that satisfy the event and enter that total as f. For example, the probability of rolling an even number on a die is f = 3 (the outcomes 2, 4, 6), so P = 3/6 = 0.5.
Yes. A fair coin has 2 total outcomes. For heads: f = 1, n = 2, so P(Heads) = 0.5 = 50%. For any specified outcome on a coin, use f = 1 and n = 2.
The complement of event E is everything that is NOT E. P(not E) = 1 − P(E). If the probability of rain is 0.3, the probability of no rain is 0.7. You can use this calculator to find P(E) and then subtract from 1 to get the complement.
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