Sample Space Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
List the sample space for rolling a fair six-sided die, and verify that all probabilities sum to 1.

Solution

  1. 1
    Identify all outcomes: S={1,2,3,4,5,6}S = \{1, 2, 3, 4, 5, 6\}
  2. 2
    Each outcome is equally likely with probability P(each)=16P(\text{each}) = \frac{1}{6}
  3. 3
    Sum all probabilities: P(1)+P(2)+P(3)+P(4)+P(5)+P(6)=6×16=1P(1)+P(2)+P(3)+P(4)+P(5)+P(6) = 6 \times \frac{1}{6} = 1
  4. 4
    Conclusion: The probabilities sum to 1, confirming a valid probability model

Answer

S={1,2,3,4,5,6}S = \{1,2,3,4,5,6\}; each with P=16P = \frac{1}{6}; total =1= 1.
A sample space contains all possible outcomes of a random experiment. The fundamental rule is that all probabilities must sum to exactly 1 — this axiom ensures the model is complete and consistent.

About Sample Space

The sample space SS is the set of all possible outcomes of a random experiment — every outcome that could conceivably occur.

Learn more about Sample Space →

More Sample Space Examples

Example 2 medium

Two coins are flipped. Write out the sample space, assign probabilities to each outcome, and find [f

Example 3 easy

A bag contains one red, one blue, and one green marble. You draw one marble. Write the sample space

Example 4 medium

A spinner has 3 sections: Red (probability 0.5), Blue (probability 0.3), and Green. Find [formula] a

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Related Concepts

Probability