Probability Calculator

Calculate the probability of events occurring based on favorable and total outcomes

Quick answer

Probability Calculator

Probability is a measure of the likelihood that an event will occur. It ranges from 0 (impossible) to 1 (certain). For example, the probability of getting heads when flipping a fair coin is 1/2 = 0.5 or 50%.

Formula

P(A) = Number of Favorable Outcomes / Total Number of Outcomes

🎲 Event Details

Quick Examples

📊 Probability Result

🎲

Enter the number of favorable and total outcomes to calculate probability!

Probability Scale

ImpossibleCertain
00.250.50.751

🎲Formula

P(A) = Number of Favorable Outcomes / Total Number of Outcomes

💡How it works

Probability is a measure of the likelihood that an event will occur. It ranges from 0 (impossible) to 1 (certain). For example, the probability of getting heads when flipping a fair coin is 1/2 = 0.5 or 50%.

ℹ️ What is Probability Calculator?

A probability calculator computes the likelihood of events occurring, whether simple (single event), compound (multiple events), or conditional (one event given another). It is used in statistics, risk analysis, game theory, insurance, and academic research.

📐 Formula

P(A) = Favorable Outcomes / Total Outcomes | P(A∩B) = P(A) × P(B)
P(A)— Probability of event A (0 to 1, or 0% to 100%)
P(A∪B)— P(A) + P(B) − P(A∩B) — Union (A or B)
P(A∩B)— P(A) × P(B) — Intersection (A and B, if independent)
P(A|B)— P(A∩B) / P(B) — Conditional (A given B occurred)

✏️ Worked Example

Event: Rolling a 5 or 6 on a die
Trials: 1 roll
  1. 1Favorable outcomes: 2 (rolling a 5 or rolling a 6)
  2. 2Total outcomes: 6 (1, 2, 3, 4, 5, 6)
  3. 3P(5 or 6) = 2/6 = 1/3 ≈ 33.3%
✅ Result: P = 1/3 ≈ 33.3%

💡 How to Interpret Results

  • ▸P = 0 means impossible; P = 1 means certain.
  • ▸Probabilities of all mutually exclusive outcomes must sum to 1.
  • ▸If P(A|B) = P(A), the events A and B are statistically independent.
  • ▸"At least one" problems are easier solved as 1 − P(none): P(at least one success) = 1 − P(all failures).
  • ▸Expected value = Σ(outcome × probability) — the long-run average result of repeated trials.

❓ Frequently Asked Questions

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