There are $N$ wires.
The $i^\text{th}$ wire has $P_i$ bulbs.
The bulbs are connected in series, so if you break a bulb, all the bulbs on the wire go out.
A person can break any lit bulb with equal probability. (Broken/Off bulbs are not included in the sample space.)
One of the wires has a parallel connection. (That means if the bulb on this wire is broken, the other bulbs still glow).
A person wants to find this wire (by breaking bulbs). If he hits a bulb in the parallel wire connection (and thereby identifies the wire) on the $X^\text{th}$ try, what is the expectation of $X$?
The total number of bulbs is $T$.