Probability Calculator
- Independent events: P(A and B) = P(A) × P(B) = 0.3 × 0.4 = 0.12.
- P(A or B) = P(A) + P(B) − P(A and B) = 0.3 + 0.4 − 0.12 = 0.58.
- P(not A) = 1 − 0.3 = 0.7 and P(not B) = 1 − 0.4 = 0.6.
- P(A given B) = P(A and B) ÷ P(B) = 0.12 ÷ 0.4 = 0.3.
- P(A and B): 0.12 (12%)
- P(A or B): 0.58 (58%)
- P(not A): 0.7 (70%)
- P(not B): 0.6 (60%)
- A only: 0.18 (18%)
- B only: 0.28 (28%)
- Exactly one of A or B: 0.46 (46%)
- Neither A nor B: 0.42 (42%)
- The four regions add up to 1 (they must total 1).
- For independent events P(A given B) = P(A): 0.3 = 0.3, confirmed.
Probability Calculator: Two Events, Single Events and Repeated Trials
This free probability calculator covers the three situations that come up most. With two events, it finds the chance that both happen, that either happens, that neither happens, and the conditional probabilities. With a single event, it turns favorable and total outcomes into a probability, a percentage and odds. With repeated trials, it finds the chance of a given number of successes. Every result comes with the working and a diagram.
Quick answer: if event A has a probability of 0.3 and event B has 0.4, and the events are independent, the chance that both happen is 0.3 × 0.4 = 0.12 and the chance that at least one happens is 0.58.
What Is Probability?
Probability measures how likely an event is, on a scale from 0, which means impossible, to 1, which means certain. It can be written as a decimal such as 0.25, a percentage such as 25%, or a fraction such as 1/4. When all outcomes are equally likely, the probability is the number of favorable outcomes divided by the total number of outcomes.
Independent and Mutually Exclusive Events
Two events are independent when one has no effect on the other, so you multiply their probabilities to find the chance of both. Events are mutually exclusive when they cannot happen together, so the chance of both is zero and the chance of either is found by adding. If you know the chance of both events from a table or survey, choose that option and enter it directly. The table shows some examples.
| Situation | Calculation | Result |
|---|---|---|
| Independent events, P(A) = 0.3 and P(B) = 0.4 | P(A and B) = 0.3 × 0.4 | 0.12 |
| Same events, A or B | 0.3 + 0.4 − 0.12 | 0.58 |
| Mutually exclusive, P(A) = 0.2 and P(B) = 0.5 | P(A or B) = 0.2 + 0.5 | 0.7 |
| Rolling an even number on a die | 3 favorable ÷ 6 outcomes | 0.5 |
| At least one six in 4 rolls | 1 − (5/6)⁴ | 0.517747 |
| Exactly 5 heads in 10 flips | C(10, 5) × 0.5¹⁰ | 0.246094 |
Conditional Probability
Conditional probability asks how likely A is once you know B has happened. It equals the chance of both, divided by the chance of B. For independent events the answer is simply P(A), because knowing B tells you nothing new. The two-event option shows P(A given B) and P(B given A) so you can compare them.
Probability, Odds and Percentages
Odds compare favorable outcomes with unfavorable ones instead of with the total. A one in six chance is a probability of 1/6, about 16.67%, but the odds for it are 1 to 5. The single-event option shows all of these forms together. For converting between them and working with ratios, the percentage calculator and the fraction calculator are useful.
Repeated Trials and the Binomial Formula
When the same chance is tried several times, such as flipping a coin ten times or testing twenty items from a production line, the binomial formula gives the chance of exactly k successes. The calculator also gives at most, at least, fewer than and more than, plus the expected number of successes and the standard deviation. For more on spread, see the standard deviation calculator and the mean, median, mode calculator.
Who Uses a Probability Calculator?
Students use it for statistics and maths homework. Teachers use it for worked examples. Game players, analysts, researchers and quality inspectors use it to judge risk and chance. For general arithmetic along the way, the scientific calculator and the math solver can help.
How to Use This Probability Calculator
Choose what to find
Pick Two events, One event or Many trials.
Enter your values
Type probabilities as decimals between 0 and 1, or use the sliders. For one event, enter the outcome counts.
Say how events are related
For two events, choose Independent, Mutually exclusive or enter P(A and B) yourself.
Read the results
See the answer, the working, a check and a diagram, with every value as a decimal and a percentage.