Chapter 13.3, Problem 46SPR

To determine

To explain:

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

‘Person has choice of black or navy blue a pair of chooses of either heels or flat.’

Answer to Problem 46SPR

The list, table and tree diagram for person to choose black or navy blue a pair of chooses of either heels or flat:

List: $\left(F,B\right),\left(F,NB\right),\left(H,B\right),\left(H,NB\right)$

Table:

Outcomes	$F$	$H$
$B$	$F,B$	$H,B$
$NB$	$F,NB$	$H,NB$

A tree diagram:

  

Explanation of Solution

Given information:

The statement:

‘Person has choice of black or navy blue a pair of chooses of either heels or flat.’

A person has two choices from among two possible outcomes for choosing a pair of shoes of types:

 • Flat: $F$

 • Heels: $H$

There are two colors for the pair of shoes as:

 • Black: $B$

 • Navy blue: $NB$

Now, a list is the sample space of 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 of choosing pair of shoes that means list is defined as:

  $\left(F,B\right),\left(F,NB\right),\left(H,B\right),\left(H,NB\right)$

A table is the sample space of all possible outcomes for the person to choose the type of shoes from two choices.

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	$F$	$H$
$B$	$F,B$	$H,B$
$NB$	$F,NB$	$H,NB$

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 pair of shoes.

The following tree diagram describes for the person choosing shoes pair is: