Define Sample Space

In basic terms, define a sample space. Give an easy example using the sample space idea.

Thanks

 

Simply, a sample space is the range of values of a random variable.
or
The collection of all possible outcomes of a probability experiment forms a set that is known as the sample space.

Definition: random experiment
A random experiment is a mechanism that produces a definite outcome that cannot be predicted with certainty. The sample space associated with a random experiment is the set of all possible outcomes. An event is a subset of the sample space.

Definition: Element and Occurrence

An event E is said to occur on a particular trial of the experiment if the outcome observed is an element of the set E .

Example 1: Sample Space for a single coin

Construct a sample space for the experiment that consists of tossing a single coin.

Solution

The outcomes could be labeled h for heads and t for tails. Then the sample space is the set: S={h,t}




Example 2 : Sample Space for a single die

Construct a sample space for the experiment that consists of rolling a single die. Find the events that correspond to the phrases “an even number is rolled” and “a number greater than two is rolled.”

Solution:

The outcomes could be labeled according to the number of dots on the top face of the die. Then the sample space is the set S={1,2,3,4,5,6}
The outcomes that are even are 2,4,and6 , so the event that corresponds to the phrase “an even number is rolled” is the set {2,4,6} , which it is natural to denote by the letter E . We write E={2,4,6} .

Similarly the event that corresponds to the phrase “a number greater than two is rolled” is the set T={3,4,5,6} , which we have denoted T .

A graphical representation of a sample space and events is a Venn diagram:

 

Perfect but like you suggested, I will put a hold on probability for now. No sense in learning two courses simultaneously.

 

learning two courses simultaneously is only for the student enrolled in undergraduate mathematics major

 

Exactly. This is not my case. Leaving probability for the future.