Chapter 6.8, Problem 16E

i.

To determine

To make a tree diagram to show all the different possible outcomes.

Answer to Problem 16E

The tree diagram with the possible outcomes can be drawn as:

  

Explanation of Solution

Given:

The table provided in the question is:

Class	Days offered
Painting	M, T, W, Th
Sculpture	T, W

Painting class is on Monday, Tuesday, Wednesday and Thursday.

Sculpture class is on Tuesday and Wednesday.

There can be only one Painting and one Sculpture class per week.

Calculation:

The tree diagram with the possible outcomes can be drawn as:

  

ii.

To determine

To find different possible schedules for the two classes.

Answer to Problem 16E

There are total of $6$ different possible schedules for the two classes.

Explanation of Solution

Given:

The table provided in the question is:

Class	Days offered
Painting	M, T, W, Th
Sculpture	T, W

Painting class is on Monday, Tuesday, Wednesday and Thursday.

Sculpture class is on Tuesday and Wednesday.

There can be only one Painting and one Sculpture class per week.

Calculation:

The tree diagram with the possible outcomes can be drawn as:

  

As conclude from the tree diagram there are total of $6$ different possible schedules for the two classes.

Hence,

There are total of $6$ different possible outcomes schedules for the two classes.

iii.

To determine

To find the probability.

Answer to Problem 16E

There are $2$ favorable outcomes.

Explanation of Solution

Given:

The table provided in the question is:

Class	Days offered
Painting	M, T, W, Th
Sculpture	T, W

Painting class is on Monday, Tuesday, Wednesday and Thursday.

Sculpture class is on Tuesday and Wednesday.

There can be only one Painting and one Sculpture class per week.

Formula used:

  $P\left(\text{event}\right)=\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}$

Calculation:

The tree diagram with the possible outcomes is shown as:

  

As from the tree diagram total number of outcomes is $6$ .

Chances of Sculpture class schedule on Tuesday from all the outcomes is $1$ .

Therefore,

  $\begin{array}{l}P\left(\text{event}\right)=\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}\\ P=\frac{1}{6}\end{array}$

Hence,

Probability of sculpture class in on Tuesday is $\frac{1}{6}$ .

iv.

To determine

To explain the statement.

Answer to Problem 16E

It is better to make a tree diagram than to use the multiplication principle because a tree diagram is a simple way of representing a sequence of events and are useful in probability since they record all possible outcomes in a clear and uncomplicated manner and in a situation like this it is better to used tree diagram since it clearly shows the outcomes and eliminates the possibilities of the event occurring on the same day.

Explanation of Solution

Given:

The table provided in the question is:

Class	Days offered
Painting	M, T, W, Th
Sculpture	T, W

Painting class is on Monday, Tuesday, Wednesday and Thursday.

Sculpture class is on Tuesday and Wednesday.

There can be only one Painting and one Sculpture class per week.

Calculation:

It is better to make a tree diagram than to use the multiplication principle because a tree diagram is a simple way of representing a sequence of events and are useful in probability since they record all possible outcomes in a clear and uncomplicated manner and in a situation like this it is better to used tree diagram since it clearly shows the outcomes and eliminates the possibilities of the event occurring on the same day.