Why does the light bulb's brightness decrease? 
The book said that the brightness of R1 would increase and R2 would decrease. I don't understand this at all.
Why does adding a wire from b to c change anything to R1? 
Shouldn't charge still flow through R1 as they should and R2's brightness decrease because the charges at point b have an alternate route to travel to point 2?
 A: The voltage drop across R2 becomes 0, and the full voltage is applied across R1 instead.
A: You ask: Shouldn't charge still flow through R1 as they should?
Well, yes, current still flows through R1 once the wire is put across b-c. But is it the same amount of current?  What determines the amount of current flowing in the whole circuit? (there are two elements: do both of them stay the same when you add the wire?)
There are specific equations that tell you:


*

*the equivalent resistance of two resistances in parallel;

*the equivalent resistance of two resistances in series; and

*how much current flows in a circuit, given the voltage and the circuit resistance.


Start by writing all three down - add them to the question here. And now apply them to the circuit without the wire in place. And then apply them with the wire  in place. This will explain why the brightness of each bulb changes.
If this only gets you part of the way, add your working to the question above, and I'll extend this answer.
