Probability > How to Use a Probability Tree Show 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.
How to draw a probability tree Can’t see the video? Click here. Why Use a probability tree? Parts of a Probability Tree DiagramA probability tree has two main parts: the branches and the ends(sometimes called leaves). The probability of each branch is generally written on the branches, while the outcome is written on the ends of the branches. Multiplication and Addition Real Life UsesProbability trees aren’t just a theoretical tool used the in the classroom—they are used by scientists and statisticians in many branches of science, research and government. For example, the following tree was
used by the Federal government as part of an early warning program to assess the risk of more eruptions on Mount Pinatubo, an active volcano in the Philippines. How to Use a Probability Tree or Decision TreeSometimes, 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 way for you to visually see all of the possible choices, and to avoid making mathematical errors. This how to will show you the step-by-step process of using a decision tree. Step 1:Draw lines to represent the first set of options in the question (in our case, 3 factories). Label them: Our question lists A B and C so that’s what we’ll use here. Step 2: Convert the percentages to decimals, and place those on the appropriate
branch in the diagram. For our example, 50% = 0.5, and 25% = 0.25. Step 3: Draw the next set of branches. In our case, we were told that 70% of factory A’s output was passenger. Converting to decimals, we have 0.7 P (“P” is just
my own shorthand here for “Passenger”) and 0.3 NP (“NP” = “Not Passenger”). Step 4:Repeat step 3 for as many branches as you are given. Step 5: Multiply the probabilities of the first branch that produces the desired result together. In our case, we want to know about the production of passenger planes, so we choose the first branch that leads to P. Step 6: Multiply the remaining branches that give the desired result. In our example 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 example, we had: .35 + .0625 + .0625 = .475 That’s it! Example 2Example Question: If you toss a coin three times, what is the probability of getting 3 heads? 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 tails). Those probabilities are represented at the ends of each branch. Next, add two more branches to each branch to represent the second coin toss. The probability of getting two heads is shown by
the red arrow. To get the probability, multiply the branches: 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: In most cases, you will multiply across the branches to get probabilities. However, you may also want to add vertically to get probabilities. For example, 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 ReferencesPunongbayan, R. et al. USGS Repository: Eruption Hazard Assessments and Warnings. ---------------------------------------------------------------------------
Need help with a homework or test question? With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. Your first 30 minutes with a Chegg tutor is free! Comments? Need to post a correction? Please Contact Us. What are the 3 components of a tree diagram?It is referred to as a tree due to its connecting lines' resemblance to branches. The components of the diagram include roots, nodes, and leaf nodes.
How does a tree diagram work?Tree diagrams display all the possible outcomes of an event. Each branch in a tree diagram represents a possible outcome. Tree diagrams can be used to find the number of possible outcomes and calculate the probability of possible outcomes.
How do you make a tree diagram in linguistics?In a tree diagram, a sentence is divided into two parts: a subject and a predicate. They are made up of noun phrases or verb phrases. These are groups of words that include a noun or verb and any words that add as modifiers. The subject is a noun phrase while a predicate is usually a verb phrase.
|