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?