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TREE DIAGRAMS

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Tree Diagrams and Possible Outcomes Tree diagrams, as the name suggests, look like a tree as they branch out symmetrically. Tree diagrams help us to visualise how many outcomes can occur They are used to help you visualise more complicated probability problems.

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Example 1 A box of chocolates is selected to check to see if any of the chocolates are faulty. Each box contains 12 soft-centres and 8 hard-centres. Two chocolates are randomly selected from the box and are tested to see if they have any faults. What is the probability of selecting two soft-centred chocolates? What is the probability of selecting a soft-centred and a hard-centred chocolate? To answer these questions, we can draw a tree diagram.

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Example 1 If we have 12 soft-centred and 8 hard-centred chocolates in a box, we have a total of 20 to choose from. When we select the first chocolate the probability of getting a soft-centre = and the probability of getting a hard-centre =. Now we can draw the first branches of the tree diagram:

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Example 1 – Tree Diagram

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You have a jar containing 6 red beads, 5 green beads and 7 yellow beads. You take out one bead at a time, note the colour and replace it. What is the probability you take a green bead?

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You have a jar containing 6 red beads, 5 green beads and 7 yellow beads. You take out one bead at a time, note the colour and replace it. What is the probability you choose two red ones in a row? 6/18 x 6/18 = 36/324 or 1/9

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Paper Scissors Rock How many outcomes does the game have? Label each possible outcome on the tree diagram as to win for a, b, or tie. Count the number of wins for A. Find the probability A will win in any round. Count the number of wins for B. Find the probability B will win in any round. Is the game fair? Do both players have an equal probability of winning any round? How does this model compare with the results you got when you played the game? How do these probabilities change when there are 3 players?

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1.At an ice cream store they have four flavors of ice cream: vanilla, chocolate, strawberry, and mint. They also have two types of toppings: sprinkles or gummy bears. They also have two types of cones to choose from: waffle cone or plain cone. Draw a tree diagram to show this information.

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What is the probability the next customer will choose a vanilla ice cream? What is the probability a customer will choose a chocolate ice cream with sprinkles on a waffle cone? Calculate the probability that a customer will buy a strawberry ice cream with gummy bears on a plain cone? Is the probability the same if the customer chooses sprinkles instead of gummy bears?

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