Chapter 8. Probability

Basic idea. The probability of an event is a number from 0 to 1. For equally likely outcomes, P(A) = (number of favourable outcomes) / (total number of outcomes) [6][12].

Rules

Complement: P(not A) = 1 − P(A)

Addition: P(A or B) = P(A) + P(B) − P(A and B)

Multiplication for independent events: P(A and B) = P(A)P(B)

Conditional probability: P(A | B) = P(A and B) / P(B)

Counting. The number of arrangements (permutations) of r items from n is P(n, r) = n!/(n − r)!. The number of selections (combinations) is C(n, r) = n!/(r!(n − r)!).

Binomial distribution. For n independent trials with success probability p, the chance of exactly k successes is C(n, k) pᵏ(1 − p)ⁿ⁻ᵏ.

Expected value. E(X) = Σ x · P(x).

Review: Two fair dice are rolled. What is the probability the sum is 7? (Answer: 6/36 = 1/6.)