(Semi)Dependent probability: 1st # is "base" prob. of event occurring, 2nd is max times it can occur

Rooble

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May 22, 2024
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This might not be the right place; it's been a long time since my high school probability. I tried searching for this issue, but couldn't find a good example where dependence is variable.

I have a list of events below, the first # is the "base" probability of that event occurring, the second is the maximum times it can occur. The model behavior is once a maximum for an event is reached, that event's probability becomes 0 and the remaining event's probabilities are increased proportional to their base probabilities.

A - 0.50% ; 1
B - 6.98% ; 2
C - 6.98% ; 2
D - 6.98% ; 2
E - 19.64% ; 7
F - 19.61% ; 8
G - 19.66% ; 9
H - 19.66% ; 9

Behavior example:
I do 3 attempts with results B, C, B. The 4th attempt's probability/remaining allowed occurrences looks like :
A - 0.54% ; 1
B - 0% ; 0
C - 7.51% ; 1
D - 7.51% ; 2
E - 21.11% ; 7
F - 21.08% ; 8
G - 21.13% ; 9
H - 21.13% ; 9

So here's the question: how do I figure out the average or expected number attempts for 1 occurrence of A?
 
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