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Formula Sheets / Maths

Chapter 30

Probability

Revise with flashcards Download this chapter (PDF) All Maths formulas (PDF)

Classical probability Conditional probability and independence Total probability and Bayes' theorem Random variables and binomial distribution

Classical probability

$P (A) = \frac{n ( A )}{n ( S )},$ $P (A^{'}) = 1 - P (A)$
Addition
$P (A \cup B) = P (A) + P (B) - P (A \cap B)$
Three events
$P (A \cup B \cup C) = \sum P (A) - \sum P (A \cap B) + P (A \cap B \cap C)$

Conditional probability and independence

$P (A ∣ B) = \frac{P ( A \cap B )}{P ( B )},$ $P (A \cap B) = P (A) P (B ∣ A)$
Independent events
$P (A \cap B) = P (A) P (B)$

Total probability and Bayes' theorem

Total probability
$P (A) = i \sum P (E_{i}) P (A ∣ E_{i})$
Bayes
$P (E_{i} ∣ A) = \frac{P ( E _{i} ) P ( A ∣ E _{i} )}{\sum _{j} P ( E _{j} ) P ( A ∣ E _{j} )}$

Random variables and binomial distribution

Mean and variance
$μ = \sum x_{i} p_{i},$ $σ^{2} = \sum x_{i}^{2} p_{i} - μ^{2}$
Binomial
$P (X = r) =^{n} C_{r} p^{r} q^{n - r},$ $q = 1 - p;$ $μ = n p, σ^{2} = n pq$

Three Dimensional Geometry Statistics