1.3. Simple and Composite Events

1. Concepts & Definitions

1.1. Experiment, observation, and sample space

1.2. Sample space: Venn and Tree diagram

1.3. Simple and composite events

1.4. Three definitions of probability

1.5. Law of large numbers and its consequences

1.6. Frequency and empirical probability

2. Problem & Solution

2.1. Coin simulator

2.2. Six-face dice simulator

2.3. Frequencies from data

2.4. Frequency of categories from tables

2.5. Simple and marginal probabilities

2.6. Conditional probabilities

2.7. Probability independence

2.8. Appyling multiplication rule

2.9. Total and Bayes Theorems

2.10. Combinations and permutations

Defining event, simple event, and composite event

An Event corresponds to a collection of one or more of the results of an experiment. It could be:

• Simple: It includes one, and only one, of the (end) results of an experiment and is represented by Ei.

• Composite: corresponds to a collection of more than one result for an experiment represented by A (set of events).

In the experiment of throwing a coin twice, let's employ a Venn Diagram to identify:

1. Simple events: All possible simple events.

2. Composite event: Identify an event A that will only occur if a head is drawn. Or that is, A = (H, H), (H, T), (T, H). Since A contains more than one result, then, is considered a composite event.

The next figure employs Venn Diagrams to illustrate the simple and composite events for this experiment.