Rate to get a R/SR card from eGacha: 5/6 (because exist a 99% chance to see 1 slot is filled with a N card, without this issue the chance is 1)
Discarding past event and N cards (and measures did by Nutkau like the fiasco with
Shuri Tsutsui), slayer cards at 2nd phase of an event are 4 (2 beta + 2 Alpha, 1SR + 1R card per tier), six if the survivor alpha cards from past event are active.
Then, sucess rate to get a R/SR slayer from eGacha (5/6)(6)[(5!)(X-5!)/(X!)]
where X is the current amount of cards in the card list and yes, that is a binomial coefficient (i spread it because i can't put those symbols in forum). The resultant rate is pretty low.
EDIT: taking count what 1 slot is filled with 1 N card.