Tree diagrams are great tools for showing independent events in probability. They help us see all the possible outcomes of different experiments, making it easier to calculate the chances of each outcome.

How to Make a Tree Diagram:

1. Start with a Point: Begin at a branching point for the first event.

2. Add Branches: Each branch shows one outcome. Make sure to label it with its probability.

3. Add More Events: For each new event, draw new branches from each outcome of the previous event.

Example:

Let’s say we are tossing a coin and rolling a die.

• Outcomes from the Coin:
  • Heads (H) – Chance of getting Heads = 1 out of 2 (or 50%).
  • Tails (T) – Chance of getting Tails = 1 out of 2 (or 50%).
• Outcomes from the Die:
  • The die can land on 1, 2, 3, 4, 5, or 6. Each outcome has a chance of 1 out of 6 (or around 16.67%).

Counting Total Outcomes:

To find the total number of branches:

Total branches = 2 (from the coin) × 6 (from the die) = 12 outcomes.

Finding the Probability of a Specific Outcome (like H and 4):

To find the chance of getting Heads and rolling a 4, you calculate:

Probability (H and 4) = Probability of H × Probability of 4

That means:

Probability (H and 4) = 1/2 × 1/6 = 1/12.

Tree diagrams make it easier to understand the chances of different combinations of independent events.