Sample spaces and events

The sample space S lists every possible outcome: it must include every outcome and list none twice. The number of outcomes is the sample size, n(S).

Examples:

• tomorrow's weather: {Rain, No Rain}, n(S) = 2;
• a match: {Win, Lose, Draw}, n(S) = 3;
• one coin: {H, T}; one die: {1, 2, 3, 4, 5, 6};
• two coins: {HH, HT, TH, TT}, n(S) = 4.

Choose the detail the question needs. For the amount of rain, use {No Rain, Drizzle, Light Rain, Heavy Rain}.

An event is a particular group of outcomes: a subset of the sample space. Think of the sample space as everyone at a party, and an event as one group of guests: 'everyone wearing red'.

• two coins, 'at least one head' = {HH, HT, TH};
• a die, 'greater than 4' = {5, 6}.

Combining two choices multiplies the counts: 3 snacks × 2 drinks = 6 combinations; a die and a coin, 6 × 2 = 12.