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Probability Calculator

Calculate probability of single and multiple events. Find P(A), P(A or B), P(A and B), and complement probabilities.

What is Probability Calculator?

A probability calculator finds the likelihood of single and combined events occurring. It calculates P(A), P(not A), P(B), P(not B), P(A and B), and P(A or B) — expressed as both percentages and fractions. Probability ranges from 0 (impossible) to 1 (certain).

How to use

  1. 1 Enter the number of favourable outcomes and total outcomes for Event A.
  2. 2 Optionally enter outcomes for Event B to calculate combined probabilities.
  3. 3 All results update instantly, showing each probability as both a percentage and a simplified fraction.
  4. 4 P(A and B) assumes the two events are independent.

Formula

P(A) = favourable outcomes / total outcomes. P(not A) = 1 - P(A). P(A and B) = P(A) × P(B) for independent events. P(A or B) = P(A) + P(B) - P(A and B).

Example calculation

Rolling a die: P(rolling a 3) = 1/6 ≈ 16.67%. Rolling two dice: P(both showing 3) = 1/6 × 1/6 = 1/36 ≈ 2.78%. P(at least one showing 3) = 1/6 + 1/6 - 1/36 = 11/36 ≈ 30.56%.

Frequently asked questions

What is the difference between P(A and B) and P(A or B)?

P(A and B) is the probability both events occur simultaneously. P(A or B) is the probability at least one of them occurs. P(A or B) = P(A) + P(B) - P(A and B).

What does it mean for events to be independent?

Two events are independent if the outcome of one does not affect the probability of the other. This calculator assumes independence when computing P(A and B).

What is the complement of an event?

The complement of event A, written P(not A), is the probability that A does not occur. P(not A) = 1 - P(A). For example, if P(rain) = 0.3, then P(no rain) = 0.7.

Can probability be greater than 1?

No. Probability is always between 0 and 1 inclusive. A value of 0 means the event is impossible; 1 means it's certain.

What is the difference between theoretical and experimental probability?

Theoretical probability is calculated from known outcomes (like a fair coin). Experimental probability is based on observed results from actual trials and may differ from theoretical values.