Answer
The brightness will not change.
Work Step by Step
Bulbs $B_1$ and $B_2$ are connected in parallel.
Bulb $B_1$ has a voltage drop of $\epsilon$ before the switch is closed.
Bulb $B_2$ has a voltage drop of $\epsilon$ before the switch is closed.
When the switch is closed, bulb B is added in parallel. It now has the same voltage drop as the bulbs that were already there, $\epsilon$. The old bulbs do not change brightness as another bulb is added in parallel.
