Make a markov system with two states:

With this numbering, we get the following transition matrix

We must calculate the number of steps to absorption. To do this, we need the fundamental matrix. First, S is the 11 matrix


Since the 1, 1 entry is 10,000, it follows that one can expect to be in state 1 10,000 times on average before absorption (including the first trip). In other words, you can expect a crash on the 10,000th trip (on average).


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