🎲 Probability Calculator

What is the Probability Calculator?

Probability measures how likely something is to happen, on a scale from 0 (impossible) to 1 (certain). The simplest case assumes every outcome is equally likely: the probability of an event is the number of favorable outcomes divided by the total number of possible outcomes. Rolling a single fair die and asking for a 4 gives 1 favorable outcome out of 6, so the probability is 1 ÷ 6, about 0.167 or 16.7%.

When you combine two events, the rules depend on whether the events are independent. Two events are independent when the outcome of one has no effect on the other, like two separate coin flips or two dice. For independent events the chance that both A and B happen is the product P(A and B) = P(A) x P(B). The chance that at least one of them happens uses the addition rule with a correction: P(A or B) = P(A) + P(B) - P(A) x P(B). The subtraction removes the double-counted overlap where both happen at once.

This calculator assumes the two events are independent, which is the most common textbook case. If the events are dependent (for example, drawing two cards without replacing the first), the multiplication rule needs a conditional probability instead, and the simple product no longer applies. Likewise, the addition rule shown here is the general one for independent events; for mutually exclusive events that can never happen together, the overlap term is zero and P(A or B) simply equals P(A) + P(B).

When to use it

• Working out the chance of rolling a specific number on a die or drawing a particular card.
• Finding the probability that two independent events both occur, such as two machines both passing a test.
• Finding the probability that at least one of two events occurs, like rain on either of two days.
• Checking homework or exam answers in a statistics or probability course.

How to use the Probability Calculator

1. Choose Single event to find a basic probability, or Two events for combined probabilities.
2. For a single event, enter the number of favorable outcomes and the total number of outcomes.
3. For two events, pick whether you are entering probabilities (0 to 1) or percentages (0 to 100).
4. Enter P(A) and P(B), then read off P(A and B) and P(A or B) in the result box.

Formula & method

Worked examples

Common single-event probabilities (equally likely outcomes)

Combining two independent events with P(A) = 0.5

Common mistakes to avoid

• Adding probabilities without removing the overlap. For P(A or B) with independent events you must subtract P(A) x P(B), otherwise you double-count the case where both happen. Simply adding P(A) + P(B) can give an answer above 1, which is impossible.
• Treating dependent events as independent. The product rule P(A) x P(B) only holds when one event does not affect the other. Drawing cards without replacement changes the totals each time, so you need conditional probability instead.
• Entering a probability greater than 1. A probability is always between 0 and 1 (or 0% and 100%). If you mean 50%, enter 0.5 in probability mode or 50 in percentage mode, not 50 in probability mode.
• Confusing "and" with "or". P(A and B) is the chance both occur and is usually the smaller number; P(A or B) is the chance at least one occurs and is larger. Make sure you are answering the question that was actually asked.

Glossary

Probability

A number from 0 to 1 measuring how likely an event is, where 0 is impossible and 1 is certain.

Favorable outcome

An outcome that counts as the event you are interested in happening.

Independent events

Two events where the outcome of one has no effect on the probability of the other.

Mutually exclusive

Two events that cannot both happen at the same time, so their overlap probability is 0.

P(A and B)

The probability that both event A and event B happen, equal to P(A) x P(B) for independent events.

P(A or B)

The probability that at least one of A or B happens, equal to P(A) + P(B) - P(A) x P(B) for independent events.

Frequently asked questions