Probability Calculator
Calculate P(A), P(A∩B), P(A∪B), P(A|B)
About the Probability Calculator
Probability turns uncertainty into a number between 0 and 1, and the way you combine events changes the math entirely. This calculator handles the four core cases: a single event, two events both happening, either event happening, and one event given another.
Students working through statistics problems use it to check answers; anyone reasoning about chance — dice, cards, risk — uses it to get the math right. It expresses each result as a decimal, a simplified fraction, and a percentage, and for single events it also gives the odds for and against, the format gamblers and bookmakers use.
How to Use the Probability Calculator
- Choose the calculation type: P(A), P(A and B), P(A or B), or P(A given B).
- Enter the total number of possible outcomes.
- Enter the favorable outcomes for event A, and for event B if your calculation needs it.
- Read the probability as a decimal, fraction, and percentage — plus the odds for single events — with the steps shown.
Why Use ToolForge’s Probability Calculator
- It covers four probability types — single, intersection, union, and conditional — rather than only the basic single-event case.
- It expresses each answer three ways (decimal, simplified fraction, percentage) and adds odds for and against on single events.
- It shows the intermediate steps, so combined probabilities are easy to follow and learn from.
- It runs in your browser instantly, with no account.
Frequently Asked Questions
What is the difference between P(A and B) and P(A or B)?
P(A and B), the intersection, is the chance both events occur. P(A or B), the union, is the chance at least one occurs, and it subtracts the overlap to avoid double-counting. The calculator handles each with the correct formula.
What is conditional probability?
Conditional probability, written P(A given B), is the chance of A occurring when B is already known to have occurred. It is found by dividing the probability of both by the probability of B, which this calculator does for you.
How are probability and odds different?
Probability compares favorable outcomes to all outcomes (say 1 in 4, or 0.25). Odds compare favorable to unfavorable outcomes (1 to 3). The calculator shows both for single events so you can switch between the two conventions.
Can a probability be greater than 1?
No. A probability always falls between 0 (impossible) and 1 (certain), and equivalently between 0% and 100%. If a calculation seems to exceed 1, the favorable outcomes have been set higher than the total — check those two inputs.
