Probability

• Probability runs from 0 (impossible) to 1 (certain); P(event) = favourable outcomes ÷ total equally likely outcomes.
• List outcomes systematically in a sample space; read probabilities from Venn diagrams.
• P(A′) = 1 − P(A); for mutually exclusive events P(A or B) = P(A) + P(B).
• Relative frequency estimates probability from data; expected frequency = probability × number of trials.
• Higher: tree diagrams — multiply along branches, add between branches.
• Higher: independent events P(A and B) = P(A) × P(B); without replacement the second probabilities change.

From impossible to certain

An outcome is one possible result; an event is a set of outcomes. Outcomes are equally likely when each has the same chance, as with a fair dice; "at random" means every item has an equal chance of being chosen.

Systematic lists

A sample space is the list of all possible outcomes. For two coins: (H, H), (H, T), (T, H), (T, T). List systematically — fix the first event and run through every option for the second — or draw a sample space diagram (a grid) for two dice.

The 1 − P rule and the addition rule

Events are mutually exclusive if they cannot happen at the same time. The probabilities of all mutually exclusive outcomes of an experiment add up to 1.

Fill from the middle out

Fill the overlap (A ∩ B) first, then the "only" regions, then the region outside both circles. ξ is the universal set; n(A) is the number of elements in A.

Probability from data

Multiply along, add between

independent