What's the difference between theoretical and experimental probability?

Theoretical probability is based on expected outcomes (a coin is 0.5 by definition). Experimental probability is based on actual results — if you flip a coin 100 times and get 47 heads, the experimental probability is 0.47. They converge as the number of trials grows.

Can probability ever exceed 1?

No. A probability of 1 means certainty, and nothing can be more certain than certain. If your calculation gives a number above 1, something went wrong in the setup — usually double-counting overlapping events.

How do I calculate the probability of at least one event occurring?

Use the complement: P(at least one) = 1 - P(none). Find the probability that the event doesn't happen at all across all trials, then subtract from 1. It's usually the easier calculation.

Probability Calculator

Calculate basic probability, combinations, permutations, and binomial distributions

Event Outcomes

Favorable Outcomes

Total Outcomes

Example: Rolling a die and getting a number ≤ 3 → favorable = 3, total = 6

Result

Enter values and click Calculate

What is the Probability Calculator?

Probability measures how likely something is to happen, expressed as a number between 0 (impossible) and 1 (certain), or as a percentage. This calculator handles common probability scenarios: single events, combined events (A and B both happening), and at-least-one problems. It's useful for students working through probability problems, anyone doing basic risk analysis, or anyone who wants to settle a debate about the odds of something happening.

How Does It Work?

Basic probability is the number of favorable outcomes divided by the total number of possible outcomes. When two events are involved, the math depends on whether they're independent or mutually exclusive.

P(A) = Favorable outcomes / Total outcomes

P(A and B) = P(A) × P(B) [if independent]

P(A or B) = P(A) + P(B) - P(A and B)

P(at least one) = 1 - P(none)

• P(A) = Probability of event A occurring

• Independent events = outcome of one doesn't affect the other

• Mutually exclusive = both events can't happen at the same time

How to Use CalciHub's Probability Calculator

1. Select the type of probability problem: single event, combined events, or complement.

2. Enter the number of favorable outcomes and total outcomes (or known probabilities).

3. Specify whether events are independent or mutually exclusive if relevant.

4. Click Calculate.

Tip: If you're not sure whether two events are independent, ask: does knowing that one happened change the probability of the other? If yes, they're dependent — the standard multiplication rule won't apply.

A Quick Example

What's the probability of rolling a 6 on a standard die twice in a row?

• P(6 on one roll) = 1/6 ≈ 0.1667

• Both rolls are independent

• P(6 and 6) = (1/6) × (1/6) = 1/36 ≈ 0.0278 or about 2.78%

Less than a 3% chance, which feels about right. Each roll feels unlikely, and two in a row is noticeably rarer, but not miraculous. That intuition lines up with the math here.

Frequently Asked Questions

It means the event is equally likely to happen or not happen — like a fair coin flip. It doesn't guarantee the event happens exactly half the time in every series of trials; it means over a large enough number of trials, it'll approach 50%.

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