Watch the video or Read the steps below to find out how to use a probability tree:
What is a Probability Tree?
Probability trees are useful for calculating combined probabilities. It helps you to map out the probabilities of many possibilities graphically, without the use of complicated probability equations.
Why Use a Probability Tree?
Sometimes you don’t 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.
Parts of a probability tree.
A probability tree has two main parts: the branches and the ends. 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
Probability Trees make the question of whether to multiply or add probabilities simple: multiply along the branches and add probabilities down the columns. In the following example (courtesy of Yale University), you can see how adding the far right 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’t just a theoretical tool used the in the classroom — they are used by scientists and statisticians in many branches of science, research and by several government bodies. 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 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 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.
How to Use a Probability Tree: Steps
Sample question: “An airplane manufacturer has three factories A B and C which produce 50%, 25%, and 25%, respectively, of a particular airplane. Seventy percent 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 case, 3 factories). Label them (our question list A B and C so that is 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 places, so we choose the first branch that leads to P.
Step 6: Multiply the remaining branches that produce 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