Sample Spaces, Tree Diagrams, and the Counting Principle

Front

What is a sample space?

Back

A sample space is the set of all possible outcomes of a probability experiment.

Front

How do you calculate the total number of outcomes using the Counting Principle?

Back

Multiply the number of choices for each decision. For example, if there are 3 choices for one decision and 4 for another, the total outcomes are 3 x 4 = 12.

Front

What is a tree diagram?

Back

A tree diagram is a visual representation that shows all possible outcomes of a series of events.

Front

If Alonzo has 2 choices for patties, 3 choices for cheese, and 2 choices for condiments, how many different cheeseburgers can he make?

Back

12 different cheeseburgers (2 x 3 x 2 = 12).

Front

What is the sample space for rolling a six-sided die?

Back

The sample space is {1, 2, 3, 4, 5, 6}.

Front

How many different outfits can you create with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

Back

80 outfits (5 x 8 x 2 = 80).

Front

What does a tree diagram help to visualize?

Back

A tree diagram helps to visualize all possible outcomes of a decision-making process.

Front

If a bag contains red, blue, green, and yellow marbles, what is the sample space when drawing one marble?

Back

The sample space is {Red, Blue, Green, Yellow}.

Front

How many variations can be created with 3 colors of flowers, 2 stem lengths, and 3 leaf types?

Back

18 variations (3 x 2 x 3 = 18).

Front

What is the formula for the Counting Principle?

Back

If there are n ways to do one thing and m ways to do another, then there are n x m ways to do both.