Numarly

Probability Calculator

Calculate probability easily with different methods

What is it?

Probability measures how likely an event is to occur, expressed as a number between 0 (impossible) and 1 (certain). This calculator supports basic probability plus complement, AND, and OR combinations of two events.

Formula

  • Basic: P = favorable outcomes / total outcomes
  • Complement: P(not A) = 1 − P(A)
  • AND (independent events): P(A ∩ B) = P(A) × P(B)
  • OR: P(A ∪ B) = P(A) + P(B) − P(A) × P(B)

Formula Explanation

Basic probability is simply the fraction of outcomes that count as a "win." The complement rule works because an event either happens or it doesn't, so the two probabilities must add to 1. The OR formula subtracts P(A) × P(B) to avoid double-counting outcomes where both events occur together.

Example Calculation

Rolling a standard six-sided die, the probability of rolling a 6 is 1/6 ≈ 0.1667 (1 favorable outcome out of 6 total).

How to Use

  1. Select the type of probability calculation you need.
  2. Enter the required values (e.g. favorable/total outcomes, or P(A) and P(B)).
  3. Click Calculate to see the probability.

Benefits

  • Covers four common probability scenarios in one calculator.
  • Shows the exact formula used alongside the result.
  • Handles independent-event AND/OR calculations without manual formula lookup.

Use Cases

  • Coin flip, dice roll, and card draw probability problems.
  • Estimating the likelihood of two independent events both occurring.
  • Homework or exam preparation involving basic probability theory.

What Your Result Means

The result is a number between 0 and 1 (or as a percentage, between 0% and 100%) representing how likely the event is. A result near 0 means the event is unlikely; near 1 means it's nearly certain.

Tips

  • Convert your decimal result to a percentage by multiplying by 100 for easier interpretation.
  • The AND formula only applies to independent events — for dependent events, you need conditional probability instead.
  • Always check that your probability inputs are between 0 and 1 before combining them.

Common Mistakes

  • Using the AND/OR formulas for dependent events, where the simple multiplication rule doesn't apply.
  • Forgetting to subtract the overlap term in the OR formula, leading to double-counting.
  • Entering probabilities as percentages (like 50) instead of decimals (like 0.5).

FAQs

What is a simple example of basic probability?

Tossing a fair coin gives P(Heads) = 1/2, and rolling a fair six-sided die gives P(rolling a 6) = 1/6.

When should I use the AND formula?

Use P(A ∩ B) = P(A) × P(B) when two events are independent — meaning one event happening doesn't affect the probability of the other.

What does the complement rule mean?

The complement rule states that the probability of an event NOT happening is 1 minus the probability that it does happen.

What does P(A ∪ B) mean?

It represents the probability that event A, event B, or both occur — the union of the two events.

Can probability be greater than 1?

No, probability is always between 0 (impossible) and 1 (certain) — a result outside that range usually indicates invalid input values.

Enter probabilities as decimals between 0 and 1, not percentages.

Last updated: July 25, 2026