Tree Diagrams: Visualizing Probability

Tree Diagrams: Visualizing Probability

Learning Objective

At the end of the lesson, you will be able to draw tree diagrams to calculate probabilities of 2 events both happening.

Introduce the learning objective and make sure students understand the goal of the lesson.

What do you already know about calculating probabilities of two events happening together?

Probability Basics

Probability is the measure of the likelihood of an event occurring. It ranges from 0 to 1, where 0 means the event will not occur and 1 means the event is certain to occur.

Explain the concept of probability and provide examples to ensure comprehension.

Dependent Events

When the outcome of one event affects the probability of another event, they are dependent events.

Define dependent events and provide examples to help students understand the concept.

Tree Diagrams

Tree diagrams are a visual tool used to show the different outcomes of a series of dependent events.

Explain what tree diagrams are and how they can be used to calculate probabilities.

Example 1

Suppose you flip a coin and roll a die. Draw a tree diagram to calculate the probability of getting tails on the coin and an even number on the die.

Walk through the example step-by-step, showing students how to draw the tree diagram and calculate the probability.

Example 2

Suppose you have a bag of marbles with 3 red and 2 blue. If you draw two marbles without replacement, what is the probability of getting a red marble and then a blue marble?

Walk through the example step-by-step, showing students how to draw the tree diagram and calculate the probability.

Practice Problems

Now it's your turn to practice! Here are some problems for you to solve using tree diagrams.

Provide students with practice problems to reinforce their understanding of tree diagrams and probability.

Conclusion

Congratulations! You now know how to draw tree diagrams to calculate probabilities of 2 events both happening. Keep practicing to improve your skills.

Summarize the key takeaways from the lesson and encourage students to continue practicing.

Write down 3 things you learned in this lesson.

Have students enter three things they learned in this lesson. With this they can indicate their own learning efficiency of this lesson.

Write down 2 things you want to know more about.

Here, students enter two things they would like to know more about. This not only increases involvement, but also gives them more ownership.

Ask 1 question about something you haven't quite understood yet.

The students indicate here (in question form) with which part of the material they still have difficulty. For the teacher, this not only provides insight into the extent to which the students understand/master the material, but also a good starting point for the next lesson.