>>> In other words, we have K/N - E, and I can't figure out how to compute 
>>> E.
>>
>> You can think of it the other way round, ie the probability of ball #1 
>> appearing after K tries is 1 minus the probability of ball #1 not 
>> occurring after K tries.
>
> Ah. So instead of a chain of non-exclusive OR events, you construct a 
> chain of independent AND events? Ingenius...

Yes, it's a useful trick to remember :-)

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