 # Probability Tree Diagram Examples

Videos, worksheets, and solutions to help Grade 6 students learn how to make and use probability tree diagrams.

Making Tree Diagrams for Possible Outcomes
Sometimes to determine the number of total outcomes, you must list all possible outcomes. A tree diagram can help you generate all the outcomes without skipping any.
Example:
Show the possible outcomes of playing the game, Rock, Paper, Scissors. Find the probability of a tie game.
Making Tree Diagrams for Possible Outcomes Part 2
Sandwich example - how many outcomes are there?
Example:
You are ordering a sandwich. Make a list of all the possibilities.
Meat - ham, turkey
Cheese - America, Provolone
Find the probability of making a sandwich with both white bread and ham.
Making Tree Diagrams for Possible Outcomes Part 3
Example of finding all the possible outcomes using a tree diagram. This one is about two spinners.
Example:
List the possible outcomes of the two spinners. Then find the P(vowel and even number)

How to draw probability tree diagrams?
Examples:
1. A bag contains 5 red sweets and 3 blue sweets. Two sweets are drawn at random (i) with replacement and (ii) without replacement. Draw a tree diagram to represent the probabilities in each case.
2. Susan has the option of taking one of three routes to work A, B or C. The probability of taking route A is 35%, and B is 25%. The probability of being late for work is she goes by route A is 10% and similarly by route B is 5% and route C is 2%. Draw a tree diagram to illustrate the probabilities.
3. A normal six-sided fair die is thrown until a six is scored and then no more throws are made. The process continues up to a maximum of three throws. Draw a tree diagram to illustrate the probabilities.
How to draw probability tree diagrams for mutually exclusive events?
Examples:
1. A bag contains 5 red sweets and 3 blue sweets. Two sweets are drawn at random with replacement. Find the probability of getting (i) 2 red sweets (ii) 2 the same color (iii) at least one red sweet.
2. A bag contains 5 red sweets and 3 blue sweets. Two sweets are drawn at random without replacement. Find the probability of different colors
How to calculate conditional probabilities using a tree diagram?
Example:
Diagnosing and treating an individual with Traft's Syndrome is a difficult process. At any given time, when an individual is experiencing three specific symptoms (temperature above 101.0°F, chest pain, and deep cough), there is a 4% chance he/she has Traft's. Out of those patients with Traft's, a recently developed treatment is found to be 85% effective in eliminating all three of these symptoms. For those patients without Traft's, the treatment is 10% effective in eliminating these three symptoms.
1. What is the probability that a particular patient has Traft's and responds positively to the treatment?
2. Imagine a patient who responds positively to the treatment (their symptoms are eliminated). What is the probability that they actually have Traft's?

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