In the Bitcoin original paper, we have two probabilities:

1- Probability of generating k number of blocks in the period T in which z confirmations are generated.

2- Probability that the attacker can ever catch up.

I can understand why we need the 1st probability, but I don't understand why we need the 2nd one. For instance, assume z=6, then in the period of T ( in which z confirmations are generated) the attacker can generate only 2 blocks, then why do need to worry if it can catch up; in fact, it couldn't catch up in this period.

Question 1: Why do we need the 2nd probability (i.e. probability of catching up)?

Question 2: what about sometimes after that period? What if it can generate enough block after z confirmations have been released and placed on top of the transaction?

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