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.

Bread - white, sourdough

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?

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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.

Sandwich example - how many outcomes are there?

Example:

You are ordering a sandwich. Make a list of all the possibilities.

Bread - white, sourdough

Meat - ham, turkey

Cheese - America, Provolone

Find the probability of making a sandwich with both white bread and ham.

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)

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.

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

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?

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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