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Probability formulas
17 formulas for Probability, from the Vectors, Probability & Statistics section of the Quantix formula library. Tap 🧮 next to a formula to solve it for any variable with step-by-step working.
| Name | Formula | Note |
|---|---|---|
| Probability | P(E) = n(E) / n(S) | 0 ≤ P ≤ 1 |
| Complement | P(E′) = 1 − P(E) | |
| Addition rule | P(A ∪ B) = P(A) + P(B) − P(A ∩ B) | |
| Mutually exclusive | P(A ∪ B) = P(A) + P(B) | |
| Conditional | P(A|B) = P(A ∩ B) / P(B) | |
| Multiplication rule | P(A ∩ B) = P(A) · P(B|A) | |
| Independent events | P(A ∩ B) = P(A) · P(B) | |
| Total probability | P(A) = Σ P(Bᵢ) P(A|Bᵢ) | |
| Bayes' theorem | P(Bᵢ|A) = P(Bᵢ)P(A|Bᵢ) / Σ P(Bⱼ)P(A|Bⱼ) | |
| Odds in favour | P(E) : P(E′) | |
| Expected value | E(X) = Σ xᵢ pᵢ | |
| Variance | Var(X) = E(X²) − [E(X)]² | |
| Binomial distribution | P(X = r) = ⁿCᵣ pʳ qⁿ⁻ʳ, q = 1 − p 🧮 Solve step by step | |
| Binomial mean / variance | μ = np; σ² = npq 🧮 Solve step by step | |
| Poisson distribution | P(X = r) = e^(−λ) λʳ / r! | mean = variance = λ |
| Normal (standardise) | z = (x − μ) / σ 🧮 Solve step by step | |
| Dice / coins | n dice: 6ⁿ outcomes; n coins: 2ⁿ outcomes |
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