Sample Space Math Example 4

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Example 4

medium
A spinner has 3 sections: Red (probability 0.5), Blue (probability 0.3), and Green. Find P(Green)P(\text{Green}) and verify the sample space probabilities sum to 1.

Solution

  1. 1
    Use the sum-to-one property: P(R)+P(B)+P(G)=1P(R) + P(B) + P(G) = 1
  2. 2
    Substitute known values: 0.5+0.3+P(G)=10.5 + 0.3 + P(G) = 1
  3. 3
    Solve: P(G)=1−0.5−0.3=0.2P(G) = 1 - 0.5 - 0.3 = 0.2

Answer

P(Green)=0.2P(\text{Green}) = 0.2
Since probabilities must sum to 1, any missing probability can be found by subtracting all known probabilities from 1. This is a direct application of the completeness axiom of probability.

About Sample Space

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

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More Sample Space Examples

Example 1 easy

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

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

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Related Concepts

Probability