"Determining a sample space and outcomes for an event: Experiment involving a single selection"

Key Concepts in Counting and Probability

Sample Space

• Definition: The sample space is the set of all possible outcomes of an experiment.
• Example: When rolling a number cube (die) with faces labeled from 1 to 6:
  • Possible outcomes: {1, 2, 3, 4, 5, 6}
  • Thus, the sample space for a single roll of the die is:
  • Sample Space: {1, 2, 3, 4, 5, 6}

Outcomes

• Definition: An outcome is a specific result that can occur when performing an experiment.
• Based on the sample space for the die roll, any face showing from 1 to 6 is an outcome.

Events

• Definition: An event is a subset of outcomes from the sample space.
• Example: For the event of rolling a 2 or 5:
  • Specific Outcomes: {2, 5}

Application Example

• Question: What is the sample space when rolling a number cube and what are the outcomes for the event of rolling a 2 or 5?
  • Answer:
  • Sample Space: {1, 2, 3, 4, 5, 6}
  • Event of rolling a 2 or 5: {2, 5}

Important Notes

• Always remember to separate outcomes with commas when listing multiple results in an event.
• Complete understanding of sample spaces and events is essential for solving problems in probability and counting.