9.03 Tables and arrays

Lesson

Worksheet

Practice

Lesson

Introduction

Two-step experiments are those that incorporate two simple experiments, for example tossing a coin and rolling a die, or tossing a coin twice. Finding probabilities of two-step experiments is easier if we use a list, table, or tree diagram to show all possible outcomes.

Ideas

Tables

Tables

A table is useful for showing all possible outcomes of two events in the rows and columns.

	1	2	3	4	5	6
\text{H}	\text{H}1	\text{H}2	\text{H}3	\text{H}4	\text{H}5	\text{H}6
\text{T}	\text{T}1	\text{T}2	\text{T}3	\text{T}4	\text{T}5	\text{T}6

For example, if we tossed 1 coin and 1 die we can show the outcomes for the coin along the first column on the left: \text{H}, \, \text{T}, and the outcomes for the die across the top row: 1, 2, 3, 4, 5, 6.

Each cell in the table is an outcome of rolling a die and a coin. There are 12 possible outcomes in the sample space.

Examples

Example 1

A player is rolling 2 dice and looking at their sum. They draw up a table of all the possible dice rolls for two dice and what they sum to.

	1	2	3	4	5	6
1	2	3	4	5	6	7
2	3	4	5	6	7	8
3	4	5	6	7	8	9
4	5	6	7	8	9	10
5	6	7	8	9	10	11
6	7	8	9	10	11	12

What is the probability the dice will sum to 8?

Worked Solution

Create a strategy

Use the formula \text{Probability}=\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}

Apply the idea

From the table we can see that there are 6\times 6=36 possible outcomes in total, 5 of which are an 8.

\displaystyle \text{Probability}

\displaystyle =

\displaystyle \dfrac{5}{36}

Substitute the values

Idea summary

A table is useful for showing all possible outcomes of two events in the rows and columns.

Outcomes

AC9M9P01

list all outcomes for compound events both with and without replacement, using lists, tree diagrams, tables or arrays; assign probabilities to outcomes