To determine the correct statement for transistor action, let's analyze each option:$\\$Option 1:$\\$Base, emitter, and collector regions should have the same size.$\\$This statement is incorrect. In a transistor, the base region is typically much thinner than the emitter and collector regions.$\\$Option 2:$\\$Both emitter junction as well as the collector junction are forward biased.$\\$This statement is incorrect. For proper transistor action, the emitter-base junction is forward biased, while the collector-base junction is reverse biased.$\\$Option 3:$\\$The base region must be very thin and lightly doped.$\\$This statement is correct. The base region in a transistor is designed to be thin and lightly doped to allow efficient transfer of charge carriers from the emitter to the collector.$\\$Option 4:$\\$Base, emitter, and collector regions should have the same doping concentrations.$\\$This statement is incorrect. The emitter is heavily doped to inject a large number of charge carriers, while the base is lightly doped, and the collector is moderately doped.$\\$Therefore, the correct option is Option 3: The base region must be very thin and lightly doped.