6th Grade Math Textbook, Fundamentals

330 Chapter 12

12-1

Sample Space

Objective To determine the sample space of an experiment • To determine the likelihood of

an event• To use a tree diagram to find the sample space for two events• To use a tree diagram

to determine the likelihood of an event

This spinner is divided into 8 equal sections. Francisco spins it once. Is it
more likely that the spinner will land on an even number or an odd number?

An is the performance of an action, such as spinning

a spinner or tossing a coin. An is the result of an experiment.

For example, any number that comes up from spinning the spinner is

an outcome. A is the collection of allpossible outcomes

in an experiment.

The sample space for Francisco’s experiment is {1, 2, 3, 4, 5, 6, 7, 8}.

An is any grouping of one or more outcomes from the sample space.

The is the chance of an event happening.

Events can be either impossible, certain, equally likely, or not equally likely.

• Events that cannothappen are.


• Events that musthappen are.


• Events that are just as likely to happen as other events are.


• Events that are notas likely to happen as other events are.
  If two events are not equally likely, one event will be more likelyto occur,
  and the other event will be less likelyto occur.

Here are some examples of events based on Francisco’s spinner:

For the sample space in Francisco’s experiment, the even numbers

are 2, 4, 6, and 8. The odd numbers are 1, 3, 5, and 7. There are the

same number of possible outcomes for spinning an even number

as for spinning an odd number.

So for Francisco’s experiment, the events of Francisco spinning an

even number and spinning an odd number are equally likely.

When all outcomes of an experiment are equally likely to occur

and an event has two or more stages, it is helpful to draw a tree

diagram. A is a visual representation that shows

all possible outcomes of one or more events. Each possible event

needs a branch so the number of branches equals the number

of possible outcomes.

Event Likelihood

spinning a 9 impossible

spinning a natural number less than 9 certain

spinning 1, 2, 3, 4 or spinning 5, 6, 7, 8 equally likely

spinning 1, 2 or spinning 4, 5, 6

not equally likely; spinning

4, 5, 6 will be more likely

than spinning 1, 2.

tree diagram

not equally likely

equally likely

certain

impossible

likelihood of an event

event

sample space

outcome

experiment

1

2

3

4

7

8

5

6