449概率中等数值题medium
Memoryless Message Relay Chain
题目
A message must traverse a chain of relay nodes to reach its destination. Each node independently takes attempts to successfully forward the message to the next node. However, on each attempt, there is an independent probability that the node permanently fails, destroying the message. If the node fails, the message is lost. If the chain has 2 nodes, find:
(i) The probability the message reaches the destination (traverses both nodes).
(ii) The expected total number of attempts across both nodes, given the message reaches the destination.
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你的答案
(i)
(ii)