Probability Calculator

Probability
16.67%
1/6 as a fraction

📊 Formats

Percentage–
Decimal–
Fraction (simplified)–
Odds–

What Is a Probability Calculator?

A probability calculator computes the likelihood of an event (or combination of events) occurring, expressed as a percentage, decimal, fraction, and odds — covering single events as well as "A and B" and "A or B" combinations.

How to Use the Probability Calculator

  1. Choose single event, "A and B," or "A or B."
  2. Enter the favorable and total outcomes for each event.
  3. For combined events, specify whether they're independent.
  4. View the result in multiple formats.

Probability Formulas

Single Event
P(A) = Favorable Outcomes ÷ Total Outcomes
A AND B (Independent)
P(A and B) = P(A) × P(B)
A OR B (Mutually Exclusive)
P(A or B) = P(A) + P(B)

Worked Example

Example: Rolling a 6-Sided Die

P(rolling a 3) = 1 favorable outcome ÷ 6 total outcomes = 1/6 ≈ 16.67%

P(rolling a 3 twice in a row, independent events) = 1/6 × 1/6 = 1/36 ≈ 2.78%

Understanding Your Results

Probability is always between 0 (impossible) and 1 (certain), or 0% to 100%. Odds express the same likelihood differently — as a ratio of favorable to unfavorable outcomes, commonly used in gambling contexts.

Independent vs. Dependent Events

Independent events don't affect each other's outcome (like separate coin flips or dice rolls). Dependent events do — for example, drawing cards from a deck without replacement changes the probabilities for subsequent draws. This calculator's "AND" mode assumes independence unless you note otherwise.

Common Mistakes to Avoid

  • Adding probabilities for events that aren't mutually exclusive without adjusting for overlap.
  • Multiplying probabilities for dependent events as if they were independent.
  • Confusing "odds" (ratio of favorable to unfavorable) with "probability" (favorable out of total).

Frequently Asked Questions

Divide the number of favorable outcomes by the total number of possible outcomes. For example, rolling a specific number on a 6-sided die is 1/6.

Probability is favorable outcomes divided by total outcomes (e.g., 1/6). Odds compare favorable to unfavorable outcomes directly (e.g., 1-to-5).

Multiply the individual probabilities together: P(A and B) = P(A) × P(B), assuming the events don't influence each other.

For mutually exclusive events (can't both happen), add the probabilities: P(A or B) = P(A) + P(B). For non-mutually exclusive events, subtract the overlap.

A probability of 0 means the event is impossible; a probability of 1 (100%) means the event is certain to happen.