How to Draw a Tree Diagram?
To make a probability tree diagram, you need to find all the possible outcomes and their associated probabilities. Follow these steps:
Step 1: Decide if the events depend on each other or happen independently.
Step 2: Draw branches to show the initial outcomes.
Step 3: Put the probabilities for each outcome on its branch.
Step 4: Draw additional branches for the next outcomes, considering if events are dependent or independent. Include the associated probabilities.
Step 5: Repeat step 4 as needed.
Step 6: To find the total probability, multiply the probabilities along the branches. The sum of these probabilities should always be 1.
For example, on rolling a six-sided die:
- The events are independent.
- Draw branches for each number (1 through 6).
- Write the probability of each number on its branch (1/6 for each).
- Draw branches for the second roll, and write the associated probabilities (again, 1/6 for each).
- Repeat if needed for more rolls.
- Multiply the probabilities along the branches to get the overall probability.
- The total of all probabilities should be 1.