## Probability Tree Diagrams: Examples How To Draw

Probability> How to Use a Probability Tree

**Probability trees** are useful for calculating combined probabilities for sequences of events. It helps you to map out the probabilities of many possibilities graphically, without the use of complicated probability formulas.

Watch the video for an example.

**Why Use a probability tree?**Sometimes you dont know whether to multiply or add probabilities. A probability tree makes it easier to figure out when to add and when to multiply. Plus, seeing a graph of your problem, as opposed to a bunch of equations and numbers on a sheet of paper, can help you see the problem more clearly.

## Bernoulli Trials And Tree Diagrams

One of the most useful applications of tree diagrams is in visualizing and solving questions related to Bernoulli Trials.

Bernoulli Trials refer to probabilistic events with only two possible outcomes, success and failure. If the probability of success is assumed to be $p$, then the probability of failure is $1-p$. In Bernoulli trials, we assume that the probability of success and failure remains the same for each trial.

There are two important questions that we are usually interested in Bernoulli Trials problems.

Both these questions can be solved using tree diagrams, as shown in the examples.

Example: Suppose a factory is producing light bulbs. The probability that any light bulb is defective is $p = 0.01$. A tester is testing light bulbs at random. What is the probability of the following events:

Solution:

Let D represents a defective light bulb and D represents a not defective light bulb.

The probability of a defective light bulb is given to be $P=0.01$. From basic probability theory, we know that:

$P=1-P=1-=0.99$.

**1. ****Finding 2 defective light bulbs:**

$P=P+P+P$

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; $ =++$.

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ; ; ; ; ;;;;;;;; $ =0.000099+0.000099+0.000099=0.000297$.

**2. Finding no defective light bulbs:**

$P=P$.

## Starting A Tree Diagram

Each tree diagram starts with an initial event, otherwise known as the parent. From the parent event, outcomes are drawn. To keep it as simple as possible, lets use the example of flipping a coin. The act of flipping the coin is the parent event.

From there, two possible outcomes can occur: drawing heads or drawing tails. The tree diagram would look like:

The tree can be extended almost infinitely to account for any additional probabilities. For example:

The second string of possibilities represents a second coin toss; the first can be either heads or tails. However, if it is heads, there are two possible outcomes for the second toss, and if it is tails, there are two possible outcomes. Now, on to calculating the probabilities.

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## This Quick Introduction Will Teach You How To Calculate Probabilities Using Tree Diagrams

Figuring out probabilities in math can be confusing, especially since there are many rules and procedures involved. Luckily, there is a visual tool called a **probability tree diagram** that you can use to organize your thinking and make calculating probabilities much easier.

At first glance, a probability tree diagram may seem complicated, but this page will teach you how to read a tree diagram and how to use them to calculate probabilities in a simple way. Follow along step-by-step and you will soon become a master of reading and creating probability tree diagrams.

## Gather Information About Your Family

Write down what you know, ask family members to fill in the gaps, and find pictures and documents. Visit libraries and online genealogy sources to search for census records, news stories, land deeds, and other documents that can verify your ancestry.

Remember that you can only go back so far because of the limited availability of reliable records. You may have heard of some people saying that they have traced their lineage all the way to Adam and Eve. But in reality, it is very hard to find accurate records older than a few hundred years because many records have been destroyed in fires, floods, acts of war, and simple negligence. Some areas of the world were better at keeping and preserving records than others, so how far you can go back will depend on where your family came from. Most family tree outlines trace ancestry back three or four generations because of the limited information.

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## You Gotta Know When To Fold Em

With your diagram in place, choose the shape whose branches you want to add the folding function to.; Once you select the shape, you should now see that the;**format panel;**on the right of your workspace has now changed to show you style options for your shape.; Click on;**Properties**, then scroll down the list until you see **Tree Folding**, and select that.

Take a look at your shape.; It should now have a;**minimize** icon on it that is clickable.; When you click, this will collapse or expand all the shapes in the branches under it.; Voilá!

## Tree Diagrams For Independent Events

**Example:**Julia spins 2 spinners; one of which is labeled 1, 2 and 3, and the other is labeled 4, 5 and 6.

a) Draw a tree diagram for the experiment.b) What is the probability that the spinners stop at 3 and 4?c) Find the probability that the spinners **do not** stop at 3 and 4.d) What is the probability that the first spinner **does not** stop at 1?

Probability that the spinners stop at =

c) The probability that the spinners do not stop at 3 and 4 Probability that the spinners do not stop at =

d) The probability that the first spinner does not stop at 1Probability that the first spinner stop at 1 = Probability that the first spinner does not stop at 1 =

**Example:**Box A contains 3 cards numbered 1, 2 and 3. Box B contains 2 cards numbered 1 and 2. One card is removed at random from each box.

a) Draw a tree diagram to list all the possible outcomes.b) Find the probability that: the sum of the numbers is 4 the sum of the two numbers is even. the product of the two numbers is at least 5. the sum is equal to the product.

**How to use probability tree diagrams for independent events ?**

**Example:**Jenny has a bag with 7 blue sweets and 3 red sweets. She picks a sweet at random from the bag, replaces it and picks again at random. Draw a tree diagram to represent this situation and use it to calculate the probabilities that she picksa) 2 red sweetsc) at least 1 blue sweetd) 1 sweet of each color

**How to do a probability tree?**

**Example:**

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## Dice Probability Using A Tree Diagram

Dice probabilities play an important role in probability theory. We usually consider multiple rolls of a six-sided fair die. The six possible outcomes of each roll, i.e., $\$ are considered to be equally likely, and every single outcome has a probability $\frac16$.;

Tree diagrams are particularly useful in solving multiple rolls of a fair die when we are interested in a particular number, e.g., questions like getting a single in 2 in three rolls or not getting a 5 in four rolls, etc. Let us consider a few examples.

**Example 2:**

We roll a single die three times. Find the probability of the following events using a tree diagram:

Solution:

Let F represent the five and F represents not a five.

The event that no five appears in all three attempts is highlighted in red in the tree diagram. We calculate the probability as follows:

$P=\frac56 \times \frac56 \times \frac56=\frac$.

There are three outcomes in the tree diagram that correspond to the event that only one five appears in three appempt. The corresponding probability is calculated as

$P = P + P + P$

$\qquad \qquad \qquad \qquad \qquad \qquad \quad = ++=\frac$.

## How Do I Make A Tree Diagram In Google Sheets

**How to make a decision tree with Google Drawings**

**Create**a new

**to Insert**> Drawing. A drawing box will appear.

**diagram**.

**Option #2: Use Google Drawings to make a Venn diagram in Google Docs**

Likewise, how do you make a tree diagram on Google Docs? **How to insert your decision tree with the Lucidchart add-on**

One may also ask, what is treemap chart?

A **treemap chart** provides a hierarchical view of your data and makes it easy to spot patterns, such as which items are a store’s best sellers. The tree branches are represented by rectangles and each sub-branch is shown as a smaller rectangle. A sunburst **chart** is a much better visual **chart** for showing that.

Is there a family tree template on Google Docs?

Then our beautifully designed and professionally made **family tree templates**. We offer a wide selection for you to choose from and all of them are readily **available** for you to download. Know that they can be opened and edited with **the** web-based application, **Google Docs**, with ease.

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## Variety Is The Spice Of Life

You dont just have the option to add a tree diagram by using the menu.; Our shape library will also get the job done right.; To add a vertical tree diagram via our shape library, click on the heading;**Advanced** in your shape library on the left side.; Select;**Vertical Tree Layout** in order to add it to your workspace.; Then when you have placed it where you need it, click on the shape you want to add the fold function to.; Exactly like with the other type of tree diagram, you can do that via by selecting the checkbox for;**Tree Folding** on the right-hand side.

## Inserting A Tree Diagram

When you have your workspace in draw.io open, go to **Arrange;**on the menu bar.; Then, head down to **Insert** then **Layout** and select one of the tree diagram types.; You may remember this from our diagramming in the fast lane with draw.io post, so refer back to that if you need a refresher!; Once the layout box appears, you can start adding branches to your tree by clicking on the blue arrow on each shape.

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## Tree Diagrams For Dependent Events

**Example:**Jimmy has a bag with seven blue sweets and 3 red sweets in it. He picks up a sweet at random from the bag, but does not replaces it and then picks again at random.Draw a tree diagram to represent this situation and use it to calculate the probabilities that he picks: two red sweets at least one blue sweet one sweet of each color

**Probability Diagrams for events that involve with and without replacements.**

**Example:**A bag contains 4 red sweets and 5 blue sweets. Draw a probability tree diagram whena) the sweets are taken with replacement.b) the sweets are taken without replacement.

**Example:**A bag contains four light bulbs, of which two are defective. We draw bulbs without replacement until a working bulb is selected. Set up the tree diagram for this experiment, find the probability of each outcome, and determine the probability that at most two draws occur.

## Option #: Use Lucidchart To Add Decision Trees Into Google Docs

Start diagramming your decision tree faster with Lucidchartâs integration with G Suite. Drag and drop shapes, use customizable templates, and include your decision tree in context with Lucidchartâs free add-on for Google Docs. For more detailed instructions, use our step-by-step guide on how to make a decision tree diagram.

*Not yet a Lucidchart user? Start your free account now.*

**How to install the Lucidchart add-on for Google Doc**

Before you can begin, youâll need to follow these steps to download the Lucidchart add-on for Google Doc.

**How to insert your decision tree with the Lucidchart add-on **

The Lucidchart add-on makes adding a high-resolution image of your decision tree to your Google Doc quick and simple.

**Create a new decision tree in Google Docs with the add-on **

Easily access the Lucidchart editor with the add-on to make your decision tree diagram and add it to your doc. Integrate data into your decision tree diagram as you consider different options to help justify your decision to others.

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## Create A Tree Diagram

With the **Block Diagram** template, you can use tree shapes to represent hierarchies, such as family trees or tournament plans.

**Note:;**Before following these steps, make sure that AutoConnect is active. On the **View** tab, in the **Visual Aids group**, the **AutoConnect** check box should be selected.

Click **File**>**New**>**Templates**>**General**, and then open **Block Diagram**.

From the **Blocks** and **Blocks Raised** stencils, drag block shapes onto the drawing page to represent stages in a tree structure.

To add text to a shape, select the shape, and then type.

Indicate relationships between the blocks by connecting the shapes:

Drag a shape from a stencil onto the drawing page and position it near another shape.

While still holding down the mouse button, move the pointer over one of the blue triangles. The triangle turns dark blue.

Release the mouse button. The shape is placed on the drawing page, and a connector is added and glued to both shapes.

**Tip:;**To reverse the direction of the arrow on a connector, see Edit connector lines, arrows, or points.

Use tree shapes to represent hierarchical stages in a tree diagram:

From **Blocks**, drag a tree shape onto the drawing page. If you want two branches, use a **Double-tree** shape. If you want two or more branches, use a **Multi-tree** shape.

Drag the endpoints on the tree shapes to connection points on block shapes. The endpoints turn red when they are glued.

## Probability Without Replacement Using A Tree Diagram

**Example:**

A bag contains 10 balls. 3 are blue, and 7 are red. A ball is drawn at random and NOT replaced in the bag. Draw a tree diagram to represent the probabilities of drawing two consecutive balls of the same color.

solution:

Notice that the probabilities of drawing a Red or Blue ball are different in the second draw as compared to the first draw. For instance, in the first draw, we have $3$ blue and $7$ red balls, so the probability of drawing a Blue ball is $\frac$. For the second draw, if we assume that a Blue ball was drawn in the first draw, then there would be $2$ Blue and $7$ Red balls left, and hence the probability of drawing another Blue ball is $\frac$, as shown in the top branch of the second draw. We calculate all the second draw probabilities using a similar argument and show them on top of their respective branches. Finally, the probability of drawing two balls of the same color is found by adding the probabilities corresponding to $$ and $$ outcomes, i.e.,

$P=P+P$

$=\frac+\frac=\frac$.

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## Anatomy Of A Decision Tree

One of the nice things about a Decision Tree Diagram is that there arenât a lot of elements. The key elements are called nodes, and appear as a square or circle with branches connecting them until a result is reached. Squares represent decisions, while circles are for uncertain outcomes.

Nodes have a minimum of two branches extending from them. On each line write a possible solution and connect it to the next node. Continue to do this until you reach the end of possibilities and then draw a triangle, signifying the outcome.

Once youâve got the basic layout of a decision tree complete, you can add values to each line to garner more intelligence. Hereâs how to do it:

1. Look at each line and add an amount to each.

2. To analyze your options numerically, add an estimate for the probability of each outcome. Note: When adding percentages all the lines from a single node need to equal 100, if youâre using fractions they need to add up to 1.

3. Assign a possible amount to each triangle at the end of the branches.

4. Calculate the results by multiplying the result by the percentage probability for each end branch in that outcome and subtract the cost of that course of action. Youâll end up with an estimate of what that particular outcome could yield.

Hereâs an example:

## What Is A Probability Tree Diagram

**Example 01:** Probability of Tossing a Coin Once

Lets start with a common probability event: flipping a coin that has heads on one side and tails on the other:

This simple probability tree diagram has two **branches**: one for each possible outcome heads or tails. Notice that the **outcome** is located at the end-point of a branch .

Also, notice that the **probability **of each outcome occurring is written as a decimal or a fraction on each branch. In this case, the probability for either outcome is *fifty-fifty*, which is 0.5 or 1/2.

**Example 02:** Probability of Tossing a Coin Twice

Now, lets look at a probability tree diagram for **flipping a coin twice!**

Notice that this tree diagram is portraying **two consecutive events** , so there is a second set of branches.

Using the tree diagram, you can see that there are four possible outcomes when flipping a coin twice: Heads/Heads, Heads/Tails, Tails/Heads, Tails/Tails.

And since there are four possible outcomes, there is a 0.25 probability of each outcome occurring. So, for example, there is a 0.25 probability of getting heads twice in a row.

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