/me not a statistician! I'm not clear how "expected no. of attempts for X" is related to the probability of X. And I seem to be struggling to recall what littl

/me not a statistician! I'm not clear how "expected no. of attempts for X" is related to the probability of X. And I seem to be struggling to recall what little I used to know about probability. I'd welcome a (link to a) clear unpacking of this scenario. I'm feeling rather stupid, as if I've had a stroke and lost a mental faculty. It seems to be a straightforward and obvious scenario, but I've lost confidence in my reasoning about it.