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# Probability Rules/Tree Diagrams

Author: Al Greene
##### Description:

• Provide examples of finding probabilities of compound events using tree diagrams

This packet introduces you to tree diagrams as a way of finding probabilities of compound events. There is a powerpoint slideshow of definitions, and a video of some examples.

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Tutorial

## What's covered in this packet

This packet introduces you to tree diagrams. Some terms that may be new are:

• Tree Diagram

Source: Greene

## Probability Rules/ Tree Diagrams

This video has the definition of a tree diagram.

Source: Greene

## Probability Rules/Tree Diagrams - Disease Example

This video shows you an example of disease test results and actual disease status.

Source: Greene

## Example

Consider the following situation:

First, you flip an unfair coin, getting either a heads or a tails, with unequal probability (p = .7 for heads, p = .3 for tails). Next, you pull a marble out of a bag. There are three colors: blue (p = .4), red (p = .5), and yellow (p = .1). Draw a tree diagram of this situation, and then figure out the probability of getting a head and a blue. Also, figure out the probability that you get a tails and a yellow.

Source: Greene

## Example solutions

Consider the following situation:

First, you flip an unfair coin, getting either a heads or a tails, with unequal probability (p = .7 for heads, p = .3 for tails). Next, you pull a marble out of a bag. There are three colors: blue (p = .4), red (p = .5), and yellow (p = .1). Draw a tree diagram of this situation, and then figure out the probability of getting a head and a blue. Also, figure out the probability that you get a tails and a yellow.

Tree Diagram:

___p = .4_____BLUE

___p = .7______H___p = .5____RED

|                                ___p = .1_____YELLOW

|

|                                       ____p = .4_____BLUE

|_____p = .3_______T____p = .5____RED

____p = .1_____YELLOW

P(H and BLUE) = We look for the heads outcome for the first event, which has p = .7. Then we see the blue probability coming off of the heads outcome is .4. Therefore, we multiply these two together. .7*.4 = .28.

P(T and YELLOW) = We look for the tails outcome for the first event, which has p = .3. Then we see the yellow probability coming off the tails outcome is .1. Therefore, we multiply these two together. .3*.1 = .03.

Source: Greene

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