Chapter 13.3, Problem 45SPR

To determine

To explain:

The list, table and tree diagram for the following statement:

‘Person has a choice of taking music lessons for the next two years and playing drums or guitar.’

Answer to Problem 45SPR

The list, table and tree diagram for person to choose music lessons for the next two years and playing drums or guitar:

List: $\left(D,D\right),\left(D,G\right),\left(G,D\right),\left(G,G\right)$

Table:

Outcomes	$D$	$G$
$G$	$G,G$	$D,G$
$D$	$G,D$	$D,D$

A tree diagram:

  

Explanation of Solution

Given information:

The statement:

‘Person has a choice of taking music lessons for the next two years and playing drums or guitar.’

A person has two choices from among two possible outcomes for music lessons for the next two years:

 • Playing drums: $D$

 • Playing guitar: $G$

Now, a list is the sample space for selection of music lesions or all possible outcomes. To make an organized list need to list the pairs of all possible outcomes in the form of first and second outcome. Therefore, for two years, the sample space is that means list is defined as:

  $\left(D,D\right),\left(D,G\right),\left(G,D\right),\left(G,G\right)$

A table is the sample space of all possible outcomes for the person to choose music lessons for next two years.

The cells of a sample space table each represent an outcome that belongs to the sample space. The following table describes the sample space for the person:

Outcomes	$D$	$G$
$G$	$G,G$	$D,G$
$D$	$G,D$	$D,D$

The sample space of outcomes for the person is represented by a tree diagram. The bottom of the diagram that means leaves of a tree represents an outcome that belongs to the sample space for the person to choose the music lessons.

The following tree diagram describes for the person choosing music lessons for two years is: