Compound Probability and Sample Spaces

What is a sample space?

The sample space is the collection of all possible outcomes of a probability experiment. Think of it as a list of everything that could possibly happen when you perform an experiment or activity involving chance.

For example, when you roll a single die, the sample space is {1, 2, 3, 4, 5, 6} because these are all the possible outcomes.

What are Compound Events?

A compound event is an event that combines two or more simple events. For instance, rolling two dice instead of one, or flipping a coin and then spinning a spinner.

When we work with compound events, the sample space gets larger because we need to account for all possible combinations of outcomes from each simple event.

Finding Sample Spaces for Compound Events

There are several methods to find and organize the sample space for compound events:

• Organized Lists: Writing out all possible outcomes in a systematic way
• Tables: Using rows and columns to show all possible combinations
• tree diagrams: Branching paths that show how choices lead to different outcomes

Calculating Compound Probabilities

Once we know the sample space, we can calculate the probability of a compound event using this formula:

For compound events, we need to:

1. Identify the complete sample space (all possible outcomes)
2. Count the total number of outcomes in the sample space
3. Identify the outcomes that represent the event we're interested in
4. Count these favorable outcomes