⭐ Sample vs. Event

Think of probability as a story with two levels:

• The sample space is the entire universe of all possible outcomes.
• An event is a subset of that universe — the part you care about.

🎯 Sample Space (S)

The sample space is the complete list of everything that could happen in an experiment.

Examples

• Rolling a die:
  
• Flipping two coins:
  
• Picking a random student:
  All students in the class form the sample space.

Key idea

The sample space is exhaustive — nothing possible is left out.

🎯 Event (A)

An event is any collection of outcomes from the sample space.
It can contain one outcome or many.

Examples

• Rolling an even number:
  
• Getting at least one head in two coin flips:
  
• Choosing a student who plays an instrument:
  A subset of the class.

Key idea

An event is something you can assign a probability to.

🧠 How they relate

• The sample space is the big set.
• An event is a smaller set inside it.
• Probability is just the size of the event relative to the size of the sample space (in equally likely cases).

🎨 A simple analogy

Sample space = the whole menu at a restaurant
Event = the vegetarian options
You’re not ordering the whole menu — just the part that matches your criteria.