Basic introduction to some terms, definitions, and laws used in probability
Chance - proportion of times event should happen over repeated trials
P(A) - proportion of times event A happens in n trials
Law of Large Numbers - as n, the number of trials, grows larger and approaches infinity, P(A) approaches
Outcome space - all possible results of a trial, P(outcome space) = 1 for any trial (i.e. the probability of a quarter flipping either heads or tails up is 100%, or 1). The probability of an impossible result is 0.
Complement of an event A - all events not including A, with total probability of 1 - P(A)
Union of events A and B - any event that includes event A, event B, or both A and B.
Intersection of events A and B - any event that includes both A and B
Partition - an event can be partitioned into non-intersecting sub-events (event A partitioned into sub-events A1, A2...An). If the probability of the intersection of sub-events is 0 (no sub-events overlap) then A1, A2...An form a partition.
Rules of Probability -
Probability of any event within the outcome space is at least 0. (P(A) ≥ 0)
If the sub-events A1, A2...An form a partition of the event A, then P(A) = P(A1) + P(A2) + ... + P(An)
Probability of the outcome space is 1; the sum of the probability of all possible and impossible events within the outcome space is 1.
Distribution - a function that divides the probability of outcome space into subsets in such a way that satisfies the rules of probability.
For example, the distribution of a coin toss is P(Heads) = 0.5, P(Tails = 0.5).