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
2.4. Frequency of categories from tables
2.5. Simple and marginal probabilities
2.6. Conditional probabilities
Another possible manner to represent the possible results of an experiment is Venn Diagram. A Venn Diagram corresponds to a rectangle, a square, or a circle that contains bullets representing all possible results of an experiment. The next Figure illustrates a Venn and Tree Diagram for the Experiment of throwing a dice in which the head (H) face event has the probability p of happening and probability 1-p of happening tail (T) face.
Probability trees are useful for calculating combined probabilities for sequences of events. It helps you to map out the probabilities of many possibilities graphically, without the use of complicated probability formulas. The next figure shows the possible results from an experiment with dice thrown twice with a Tree diagram and its corresponding Veen Diagram.