At a certain research institute, records show that Event A corresponds to the scenario in which a newly admitted scholar chooses to attend the "Specialized Seminar on Advanced Analytics." Meanwhile, Event B is the case where the same scholar simultaneously subscribes to the "Monthly Research Digest."
It is known that the numerical likelihood of Event A materializing has been empirically established to be 0.42. Likewise, the statistical chance of Event B occurring has been separately archived as 0.68.
Now, two contradictory reports have been issued:
* One department insists that whether a scholar attends the Seminar (Event A) has absolutely no statistical bearing on whether the same scholar subscribes to the Digest (Event B) — essentially treating them as "probabilistically autonomous phenomena."
* However, a survey conducted on actual participants reports that, conditional upon the scholar having already subscribed to the Digest (Event B), the chance of simultaneously being in the Seminar (Event A) is recorded as 0.77.
Keeping in mind that you should treat these two perspectives separately, and ignoring all additional information not directly relevant, answer the following:
1. If we go with the autonomy (independence) assumption, what is the precise probability that both Event A and Event B occur together?
2. If we instead trust the survey's conditional assessment, what is the probability that both Event A and Event B occur together?
