How do I calculate the probability of a single event?

Divide the number of favorable outcomes by the total number of equally likely outcomes. Probability ranges from 0 (impossible) to 1 (certain), and multiplying by 100 expresses it as a percentage.

How do I find the probability of two events both happening?

For independent events, multiply their probabilities: P(A and B) = P(A) x P(B). Two coin flips both landing heads is 0.5 x 0.5 = 0.25. If the events are dependent, use the conditional probability of the second given the first.

How do I calculate the probability of A or B?

Use the addition rule: P(A or B) = P(A) + P(B) - P(A and B). Subtracting the overlap prevents double-counting outcomes where both events occur.

What is the complement rule?

The probability an event does not happen is 1 minus the probability it does. It's especially useful for 'at least one' problems: P(at least one success) = 1 - P(no successes).

What is the difference between combinations and permutations?

Permutations count arrangements where order matters (nPr); combinations count selections where it doesn't (nCr). Choosing 3 committee members from 10 people is a combination; ranking 3 winners is a permutation.

Probability Calculator

Calculate probability of events, combinations, and statistical outcomes. Free, fast, accurate — no signup, mobile-friend

Probability Type

Parameters

Favorable Outcomes

Total Possible Outcomes

🎲 Common Examples

📏 Probability Rules

• 0 ≤ P(A) ≤ 1 (probabilities are between 0 and 1)

• P(A') = 1 - P(A) (complement rule)

• P(A ∪ B) = P(A) + P(B) - P(A ∩ B) (addition rule)

• P(A|B) = P(A ∩ B) / P(B) (conditional probability)

Probability

0.1667

16.67%

Complement

0.8333

83.33%

Odds For

0.2

to 1

Odds Against

to 1

Likelihood: Unlikely

10-30% chance

Step-by-Step Solution

1Given: Favorable outcomes = 1, Total outcomes = 6

2Basic probability formula: P(A) = favorable outcomes / total outcomes

3P(A) = 1 / 6 = 0.1667

How it works

Probability measures how likely an event is, from 0 (impossible) to 1 (certain). For equally likely outcomes it's the number of favorable outcomes divided by the total. Independent events combine by multiplying; mutually exclusive ones by adding.

Basic probability

P(event) = favorable outcomes ÷ total outcomes        P(A and B) = P(A) × P(B)   (independent)

favorable: outcomes that count as the event
total: all equally likely outcomes

Worked example

Roll one die; event = rolling a 4 or higher

Favorable outcomes: 4, 5, 6 → 3
Total outcomes: 6

P = 3 ÷ 6 = 0.5 (50%).

Good to know

Probabilities always fall between 0 and 1 (or 0–100%).
The complement rule is handy: P(not A) = 1 − P(A).
For “A or B” that can both happen, subtract the overlap: P(A) + P(B) − P(A and B).