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The bulb you remove will go out :)

Overall current will also be reduced proportional to the resistance of the bulb being removed.

Lets say you have two 60 W incandescent bulbs in parallel and they each are drawing 1/2 Amp (60W = 120 Volts x 1/2 Amp). The resistance of each bulb is 240 Ohms (120 Volts / .5 Amps). The parallel resistance is 120 Ohms so 1 Amp is being drawn. When one of the two bulbs is removed the resistance changes from 120 Ohms to 240 Ohms, reducing the current from 1 Amp to 1/2 Amp.

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