# Define Sample Space

Discussion in 'Probability and Statistics' started by nycmathguy, Jul 6, 2021.

1. ### nycmathguy

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

Thanks

nycmathguy, Jul 6, 2021
2. ### MathLover1

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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:

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MathLover1, Jul 6, 2021
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3. ### nycmathguy

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

nycmathguy, Jul 6, 2021
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4. ### MathLover1

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

MathLover1, Jul 6, 2021
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