1. Tree Diagrams
Section 5

2. Counting Principle
If one experiment has M different outcomes and another experiment has N different outcomes, then the combination of both experiments, one after the other, has M·N different outcomes.
Example: At a restaurant, you may have 3 different choices for a main entree and 5 different choices for a side. In all, you have 3·5 = 15 different possibilities for meals!

3. Tree Diagrams
Sometimes, when applying the counting principle, it can be difficult to determine the number of possibilities that can arise, based on how complicated the experiments are.
It can be helpful to make a visual diagram to help list all of the possible outcomes of an experiment.
Tree diagrams are often a helpful way of produce complete lists of the outcomes of the combinations of multiple experiments.

4. Steak Outcomes Fish Chicken Fries Salad Coleslaw Soup Baked Potato
Steak + Fries
Salad
Steak + Salad
Steak
Coleslaw
Steak + Coleslaw
Soup
Steak + Soup
Outcomes
Baked Potato
Steak + Baked Potato
Fries
Fish + Fries
Salad
Fish + Salad
Fish
Coleslaw
Fish + Coleslaw
Soup
Fish + Soup
Baked Potato
Fish + Baked Potato
Fries
Chicken + Fries
Salad
Chicken + Salad
Chicken
Coleslaw
Chicken + Coleslaw
Soup
Chicken + Soup
Baked Potato
Chicken + Baked Potato

5. With or Without Replacement
When performing the same experiment multiple times, there are two ways of doing so:
With replacement - outcomes from one experiment are still available in the next experiment
Examples: die rolls, coin flips, spinners, drawing cards from a deck and shuffling the card back in
Without replacement - outcomes from early experiments won’t be available in later experiments
Examples: drawing balls from urns and not putting them back in, drawing cards from a deck and leaving them out