Question

probability and sample space diagrams
as the number of possible outcomes for two events increases it can be difficult to keep everything organized using tree diagrams. another way to show all possible outcomes is to use a sample space diagram, or sample space. lets take a look at one below.
example: a single die is rolled twice. the result of 1 die roll wont affect the other. the outcomes, or events, of one die go across, while those of the other go down. all the possible combinations between the 2 events can be seen as intersections of rows and columns.
notice how each row is labeled based on each side of a die, and each column is labeled by each side of the other die. because there are 6 rows and 6 columns there are 6×6 or 36 possible outcomes.
try this: fill in the possible outcomes for the cards and spinner below.
heart club diamond spade

Explanation:

Step1: Identify number of outcomes for each event

There are 4 types of cards (heart, club, diamond, spade) and 3 sections on the spinner (1, 2, 3).

Step2: Calculate total number of combinations

By the multiplication principle, the total number of possible outcomes is the product of the number of outcomes of each event. So, $4\times3 = 12$ possible combinations.

Step3: Fill in the sample - space diagram

For row 1 (spinner outcome 1): Heart - 1, Club - 1, Diamond - 1, Spade - 1
For row 2 (spinner outcome 2): Heart - 2, Club - 2, Diamond - 2, Spade - 2
For row 3 (spinner outcome 3): Heart - 3, Club - 3, Diamond - 3, Spade - 3

Answer:

	Heart	Club	Diamond	Spade
2	Heart - 2	Club - 2	Diamond - 2	Spade - 2
3	Heart - 3	Club - 3	Diamond - 3	Spade - 3