Probability basics (definitions & rules)
Random phenomenon — outcome uncertain but with a regular distribution over many repetitions. Probability model — (1) sample space S (all possible outcomes) and (2) probabilities for each outcome. Event — set of outcomes of interest (e.g., “< 3 on a die”). Disjoint (mutually exclusive) — A and B cannot happen together. Independent — occurrence of A does not affect probability of B (coin tosses, etc.). |
Probability basics (definitions & rules)
1. Bounds - 0 ≤ P(A) ≤ 1 | Probabilities can’t be negative or >1 | If you ever get >1, check math! 2. Certainty - P(S)=1 | Something must happen | “Whole sample space = 1” 3. Complement - P(A^c)=1−P(A) | If P(rain)=0.2, P(no rain)=0.8 | Useful for “at least one” problems 4. |
