Help needed with multi variable events

I hope this is the right place to ask this question.

I have large number of events

Each event has 8 variables which are independent.

Each event has 3 possible results, and in this instance I'm only interested in result A

Each variable occurs X% of the time, and when each variable occurs A occurs Z% of the time.

Given the 8 variables are a-h, what % of the time will all 8 variables occur at the same? And what will Z be when all variables occur?

I hope all that makes sense

Thanks in advance

Supay