# 4: 3. Sample Spaces

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The following topics are included in this series of five videos.

1. Introduction to Sample Spaces
2. Sample space, example 2
3. Sizes of sample spaces and the multiplication principle
4. Sizes of sample spaces, example 2
5. Sizes of sample spaces, example 3

An outcome is a possible result from an experiment. A sample space is the set of outcomes of an experiment.

The sample space is $$S=\{RR, RPRPP, RPP, PRR, PRPRPP, PRPP, PP\}$$.

The sample space is $$S=\{WWW, WWT, WWL, WT, WL, T, LW, LT, LLW, LLT, LLL\}$$.

#### PREWORK:

1. Consider the following experiment. A caterer offers 6 appetizers, 4 entrees, and 5 desserts. A menu consists of an appetizer, an entree, and a dessert. A customer chooses a menu for the big party to celebrate her 19th birthday. What is the size of the sample space for this experiment? (In other words, how many different menus are possible?)
2. A jar contains two red and four purple balls. Balls are selected one after the other without replacement until two consecutive balls of the same color are chosen. Draw a tree diagram and write the sample space for this experiment.

#### Solutions

1. This experiment has three stages (appetizer, entree, dessert) and the choice made in any one stage doesn't affect the number of choices at any other stage. Therefore we can use the multiplication principle to get $$6\cdot 4\cdot 5=120$$ different menus.

2. I drew the tree diagram in one of the videos above (oops!). The sample space is $$S=\{RR, RPRPP, RPP, PRR, PRPRPP, PRPP, PP\}$$.

4: 3. Sample Spaces is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.