Answer: The brightness of each bulb would remain the same even though the total resistance of the circuit would decrease.
Explanation:
When equal resistance bulbs are connected in parallel, the equivalent resistance of the circuit decreases.

The voltage across each bulb would remain same as all the bulbs are connected across the same potential difference.
The brightness of the bulb would not vary. This is because, with increase in the number of bulbs connected in parallel, the voltage drop across each bulb would remain unchanged. Since each bulb has same resistance, same current would be drawn and thus, there would be no change in the brightness.
V = IR ( Ohm's Law)
Although, the net resistance of the circuit would decrease and current drawn from the battery would increase but power drawn (P = V I) would remain same by each bulb unchanging the brightness of the bulb.