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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

1. Representing Sample Spaces

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Exercise 30 Page 888

A tree diagram displays all of the possible outcomes, while the Fundamental Counting Principle only allows us to find the number of possible outcomes in a sample space.

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Practice makes perfect

A tree diagram and the Fundamental Counting Principle play different roles in describing the sample space of an experiment. First, we can use a tree diagram to display all of the possible outcomes together with their probabilities. Let's consider an example of flipping a coin 3 times.

tree diagram of flipping a coin 3 times

Here we have all elements of a sample space listed at the bottom of a tree diagram. Now, using the Fundamental Counting Principle we can calculate the number of possible outcomes for this experiment. To do this we will multiply the number of possible outcomes from each stage. In our example in each of the three stages we have 2 possible outcomes. 2* 2* 2_3=8 The number of possible outcomes from this experiment is 8. Therefore, if we are interested only in the number of possible outcomes, then using the Fundamental Counting Principle will be sufficient. However, if we need to list the entire sample space we will need to use a tree diagram.

Subchapter links

Exercises p.886-889