Probability and Combinatorics Flashcards

Grade 10 · Math · Flashcards

Core formulas and rules for counting, arrangements, and calculating probability.

Flashcards

Fundamental Counting Principle: If task 1 has m ways and task 2 has n ways, both together have m × n ways.
Permutation P(n,r): Ordered selection of r from n: P(n,r) = n!/(n−r)!.
Combination C(n,r): Unordered selection of r from n: C(n,r) = n!/[r!(n−r)!].
Permutations with Identical Items: n items with groups of a, b, c identical items: n!/(a!b!c!).
Circular Permutations: Arranging n distinct items in a circle: (n−1)! ways.
Sample Space: The set of all possible outcomes of an experiment.
Probability Rule: 0 ≤ P(A) ≤ 1 for any event A; P(certain event) = 1; P(impossible event) = 0.
Complement Rule: P(A') = 1 − P(A).
Addition Rule (general): P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
Mutually Exclusive Events: P(A ∩ B) = 0; P(A ∪ B) = P(A) + P(B).
Independent Events: P(A ∩ B) = P(A) × P(B); occurrence of one does not affect the other.
Conditional Probability: P(A|B) = P(A ∩ B)/P(B); probability of A given B occurred.
Expected Value: E(X) = Σ[x × P(X=x)]; the long-run average outcome of a random variable.
Pascal's Triangle Row n: Row n gives C(n,0), C(n,1), ..., C(n,n) — the binomial coefficients for (a+b)ⁿ.