What you’ll learn
Represent compound events with tree diagrams.
Key idea
Alternative first branches contribute separate groups of terminal paths; groups add, unlike consecutive stage choices.
Alternative branch groups add; a complete path does not traverse both alternatives.
Worked example
Enter the exact value or ordered values in the format requested below.
Two-stage tree: Start→R→['R1', 'R2', 'R3']; Start→B→['B1', 'B2', 'B3', 'B4', 'B5']. Enter its total terminal leaves.
- The first-stage alternative R leads to 3 leaves, while alternative B leads to 5 leaves.
- A full path takes either R or B, not both; total=3+5=8, and missing B count=8-3=5.
Answer: 8
Quick Check
Evaluate a worked attempt at represent compound events with tree diagrams, identify the first invalid step, and provide the correction.
Tree Start→R→['R1'], Start→B→['B1', 'B2', 'B3', 'B4', 'B5', 'B6']. Step1 counts 1 R leaves and 6 B leaves. Step2 multiplies groups to claim 6 full paths. Locate the first invalid step and correct the total.