Chapter 3: Reliability and Combinatorial Applications

Learning Objectives

• Model series, parallel, and complex network reliability using probability axioms and inclusion-exclusion
• Apply the probabilistic method to prove existence of combinatorial structures, including Shannon's random coding argument
• Analyze occupancy problems (balls into bins) and derive the coupon collector's expected waiting time
• Connect birthday-bound collision analysis to hash security and random access protocols
• Understand how system reliability bounds propagate into wireless network availability guarantees