Probability Calculator

Calculate probability for single events, combined events (AND/OR), and count combinations (nCr) and permutations (nPr) with step-by-step formulas.

⚡ Quick Calculator Get a fast estimate

Favourable Outcomes

Total Outcomes

Probability P(E)

0.5

As percentage

50.0000%

As fraction

3/6

Odds for (in favour)

3 to 3

Odds against

3 to 3

Complementary P(not E)

0.5

Link copied to clipboard!

How to Use

Single Event: Enter favourable outcomes and total outcomes.
Multiple Events: Enter P(A) and P(B) — choose independent or mutually exclusive.
nCr / nPr: Enter n (total) and r (chosen) to find combinations and permutations.

The Extended Calculator adds a probability tree diagram, conditional probability, and Bayes' theorem. The Professional Calculator covers binomial distribution, normal distribution with shaded area SVG, expected value, and Monte Carlo simulation.

Need more detail?

📊 Extended Calculator More options, charts, and scenario comparison

Probability of success (p)

Number of trials (n)

Number of successes (k)

Probability Results

P(success) = p

0.3 (30.0000%)

P(failure) = q = 1-p

0.7 (70.0000%)

P(exactly 2 in 5)

0.3087 (30.8700%)

P(at least 1 in 5)

0.83193 (83.1930%)

Expected successes

1.5

Standard deviation

1.024695

Probability Formulas

P(E) = Favourable outcomes / Total outcomes

P(A AND B) — independent: P(A) × P(B)

P(A OR B): P(A) + P(B) − P(A AND B)

Conditional: P(A|B) = P(A AND B) / P(B)

Bayes: P(A|B) = P(B|A) × P(A) / P(B)

Combinations nCr: n! / (r! × (n−r)!)

Worked Example

Rolling a 4 on a die: P = 1/6 ≈ 16.67%

Heads AND heads on two coins: P = 0.5 × 0.5 = 25%

SA Lotto C(52,6): 52! / (6! × 46!) = 20,358,520 combinations

P(jackpot with 1 ticket) ≈ 1 in 20.4 million

Need full precision?

🔬 Professional Calculator Complete parameters, sensitivity analysis, and detailed breakdown

Trials (n)

Success probability (p)

Successes of interest (k)

B(10, 0.5) — k = 5

24.6094%

P(X = 5)

0.246094

P(X ≤ 5)

0.623047

P(X ≥ 5)

0.623047

Mean μ = np

SD σ = √(npq)

1.581139

Frequently Asked Questions

Combinations count selections where order does NOT matter (choosing 3 players from 10). Permutations count arrangements where order DOES matter (1st, 2nd, 3rd place). Permutations ≥ combinations — each combination can be arranged in r! ways.

Two events are independent if the outcome of one doesn't affect the other. Flipping a coin and rolling a die are independent. Drawing two cards without replacement are NOT independent.

Two events are mutually exclusive if they cannot both happen simultaneously. Rolling a 3 or rolling a 5 on one die roll. For these: P(A OR B) = P(A) + P(B).

Choose 6 from 1–52: C(52,6) = 20,358,520 combinations. Jackpot probability ≈ 1 in 20.4 million with one ticket.

P(A|B) is the probability of A given B has occurred. Formula: P(A|B) = P(A AND B) / P(B). Bayes' theorem reverses the conditioning: P(A|B) = P(B|A) × P(A) / P(B).

Probability Calculator

How to Use

Probability Formulas

Worked Example

Frequently Asked Questions

Related Calculators