13.2.1 Probability Theory involving Equally Likely Outcomes (1) - Mathematics

13.1 Sample Space

(A) Experiment

1. An experiment is a process or an action in making an observation to obtain the required results.

2. The result of the experiment is called the outcome.

(B) Listing all the possible outcomes of an experiment

We can list all the possible outcomes of an experiment by carrying out the experiment or by reasoning.

Example 1:

Six cards as shown in the diagram above are placed in a box. A card is drawn at random from the box. List all the possible outcomes.

Solution:

All the possible outcomes are O, R, A, N, G, E.

(C) Sample space of an experiment

1. A sample space is the set of all the possible outcomes of an experiment.

2. The letter S is used to represent the sample space and all the possible outcomes are written in brackets, { }.

Example 2:

A letter is chosen from the word ‘GARDEN’.

(a) List all the possible outcomes.

(b) Write the sample space, S, using set notation.

Solution:

(a) The possible outcomes are G, A, R, D, E and N

(b) Sample space, S = {G, A, R, D, E, N }