How to Find the Number of Probable Paths
In probability and statistics, you may be asked to find the total number of paths to a certain result. For example, you might have to calculate how many ways particular cars can be manufactured or how many different paths there are to achieving an educational goal. One solution to this often-tricky problem is to draw a tree diagram. A tree diagram can help you see all of the possible paths and solutions to a problem.
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Instructions
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Draw the starting point for your problem on the left-middle side of the page. For example, if you wanted to know how many possible ways there were to travel from New York city to Acadia, California, via Los Angeles, write "New York City" on the left middle of the page.
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Write down the number of paths you can take to get from your first destination to your second. These paths should be placed slightly to the right of your starting point and connected to the starting point by lines, representing branches of a tree. In this example, you might write "car," "train," "bus" and "plane."
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Write down the number of ways you can get from your second to your third destination, slightly to the left of the column you drew in the previous step. In this example, the first branch of your tree leads to "car" and you can get to Acadia by car, plane or bus. Write these three options as branches coming out from "car." The second branch leads to "train" and you can also get to Acadia by car, plane or bus. Write these three options as branches coming out from "train." Repeat for the bus and plane branches.
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Continue mapping out the paths for any remaining possibilities until you reach your destination point.
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Count the number of paths you can take from your starting point to your destination point, using the tree as a guide. In this example, there are 12 ways to get to Acadia from New York City: car, train; car, plane; car, bus; bus, car; bus, plane; bus, bus; plane, bus, plane, car; plane, plane; train, car; train, plane and train, bus.
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Tips & Warnings
Although this is called a "tree" diagram, it doesn't really resemble a tree, as the movement on the paper is from left to right. In order for it to look like a tree, place your starting point at the bottom of the paper and move upwards.
