Probability Calculator

Calculate probabilities for single events, multiple events, combinations, and permutations. See formulas and visual breakdowns.

Single Event Probability

Number of Favorable Outcomes

Total Number of Outcomes

16.67%

Probability

1/6

Fraction

1:5

Odds (for:against)

0.1667

Decimal

83.33%

Not Happening

16.67%

P(A) = 1 / 6 = 0.1667

Multiple Events

P(A) — Probability of Event A (%)

P(B) — Probability of Event B (%)

Results (Independent Events)

15%

P(A AND B)

65%

P(A OR B)

50%

P(NOT A)

70%

P(NOT B)

P(A ∩ B) = P(A) × P(B) = 0.5 × 0.3 = 0.15

Conditional Probability

P(A|B) = P(A ∩ B) / P(B)

P(A ∩ B) — Both events occur (%)

P(B) — Event B occurs (%)

50%

P(A | B) — Probability of A given B

P(A|B) = 15% / 30% = 50%

Combinations (nCr)

Order does NOT matter

n — Total items

r — Items to choose

120

Combinations

C(10,3) = 10! / (3! × 7!) = 120

Permutations (nPr)

Order DOES matter

n — Total items

r — Items to arrange

720

Permutations

P(10,3) = 10! / 7! = 720

Bayes' Theorem

P(A|B) = P(B|A) × P(A) / P(B)

P(A) — Prior probability (%)

P(B|A) — Likelihood (%)

P(B) — Evidence (%)

18%

P(A | B) — Posterior Probability

P(A|B) = (90% × 1%) / 5% = 18%