Probability Tree Diagrams: Examples, How to Draw

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Probability > How to Use a Probability Tree
Probability trees are utilitarian for calculating combine probabilities for sequences of events. It helps you to map out the probabilities of many possibilities graphically, without the use of complicate probability formulas .
Watch the video for an case.
How to draw a probability treeHow to draw a probability tree Watch this video on YouTube
Can’t see the video? Can ’ thyroxine see the television ? Click hera Why Use a probability tree?
Sometimes you don ’ triiodothyronine 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 crowd of equations and numbers on a plane of newspaper, can help you see the problem more clearly .

Parts of a Probability Tree Diagram

A probability tree has two main parts : the branches and the ends ( sometimes called leaves ). The probability of each branch is broadly written on the branches, while the consequence is written on the ends of the branches.
probability tree

Multiplication and Addition
Probability Trees make the question of whether to multiply or add probabilities simple : reproduce along the branches and add probabilities down the column. In the follow example ( from Yale University ), you can see how adding the far proper column adds up to 1, which is what we would expect the sum total of all probabilities to be :
.9860 + 0.0040 + 0.0001 + 0.0099 = 1

Real Life Uses

probability trees aren ’ triiodothyronine just a theoretical tool used the in the classroom—they are used by scientists and statisticians in many branches of skill, research and government. For exercise, the take after tree was used by the federal government as region of an early warn program to assess the gamble of more eruptions on Mount Pinatubo, an active volcano in the Philippines.

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How to Use a Probability Tree or Decision Tree

sometimes, you ’ ll be faced with a probability question that just doesn ’ t have a simple solution. Drawing a probability tree ( or tree diagram ) is a direction for you to visually see all of the possible choices, and to avoid making mathematical errors. This how to will show you the bit-by-bit process of using a decision tree.
How to Use a Probability Tree: Steps
Example question : An airplane manufacturer has three factories A B and C which produce 50 %, 25 %, and 25 %, respectively, of a particular airplane. Seventy percentage of the airplanes produced in factory A are passenger airplanes, 25 % of those produced in factory B are passenger airplanes, and 25 % of the airplanes produced in factory C are passenger airplanes. If an airplane produced by the manufacturer is selected at random, calculate the probability the airplane will be a passenger plane .
Step 1: Draw lines to represent the first set of options in the question ( in our shell, 3 factories ). Label them : Our question lists A B and C so that ’ s what we ’ ll practice here .
Step 2: Convert the percentages to decimals, and place those on the appropriate arm in the diagram. For our case, 50 % = 0.5, and 25 % = 0.25.
how to use a probability tree

Step 3: Draw the following set of branches. In our casing, we were told that 70 % of factory A ’ mho output was passenger. Converting to decimals, we have 0.7 P ( “ P ” is just my own shorthand hera for “ Passenger ” ) and 0.3 NP ( “ NP ” = “ not Passenger ” ).
Making a probability tree branch

Step 4: Repeat gradation 3 for american samoa many branches as you are given .
prob tree 3

Step 5: Multiply the probabilities of the first branch that produces the coveted result together. In our sheath, we want to know about the production of passenger planes, so we choose the first branch that leads to P.
probability tree 4

Step 6: Multiply the remaining branches that give the coveted result. In our exercise there are two more branches that can lead to P.

Step 6: Add up all of the probabilities you calculated in steps 5 and 6. In our exercise, we had :
.35 + .0625 + .0625 = .475
That ’ s it !

Example 2

Example Question: If you toss a coin three times, what is the probability of getting 3 heads ?
tree diagram 1

The first step is to figure out your probability of getting a heads by tossing the coin once. The probability is 0.5 ( you have a 50 % probability of tossing a heads and 50 % probability of tossing a chase ). Those probabilities are represented at the ends of each branch .
tree diagram 2

Next, add two more branches to each branch to represent the second coin pass. The probability of getting two heads is shown by the red arrow. To get the probability, multiply the branches :
0.5 * 0.5 = 0.25 ( 25 % ).
This makes feel because your potential results for one mind and one buttocks is HH, HT, TT, or TH ( each combination has a 25 % probability ) .
tree diagram 3

Finally, add a third row ( because we were trying to find the probability of throwing 3 heads ). Multiplying across the branches for HHH we get :
0.5 * 0.5 * 0.5 = 0.125, or 12.5 % .
tree diagram 4

In most cases, you will multiply across the branches to get probabilities. however, you may besides want to add vertically to get probabilities. For case, if we wanted to find out our probability of getting HHH OR TTT, we would first calculated the probabilities for each ( 0.125 ) and then we would add both those probabilities : 0.125 + 0.125 = 0.250 .
Tip: You can check you drew the tree correctly by adding vertically : all the probabilities vertically should add up to 1 .
Next : Tree Diagram Real Life Example


Punongbayan, R. et alabama. USGS repository : Eruption Hazard Assessments and Warnings.

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