function of resistors in transistor switch
Follow the schematic simplifications below by following the direction of the blue arrows:







simulate this circuit &ndash; Schematic created using CircuitLab

The bottom schematic is the analysis equivalent. The Kirchoff's voltage law then provides:

$$4\frac{R_2}{R_1+R_2}-I_\text{B}\cdot R_X-V_\text{BE}=0\:\text{V}$$

Therefore:

$$I_\text{B}=\frac{4\frac{R_2}{R_1+R_2}-V_\text{BE}}{R_3+\frac{R_1\: R_2}{R_1+R_2}}$$

Typically, for a switch use, deep saturation is assumed and therefore \$\beta\approx 10\$ is typical. You can choose a different value. But this is a commonly accepted value.

If you know the intended lamp current when operating near \$4\:\text{V}\$ then you can work out that you need \$I_\text{B}=I_\text{LAMP}\frac{1}{\beta=10}\$.

So:

$$I_\text{LAMP}=\frac{4\frac{R_2}{R_1+R_2}-V_\text{BE}}{R_3+\frac{R_1\: R_2}{R_1+R_2}}\cdot\left(\beta=10\right)$$

This establishes all your relationships for the resistors. From there, you should be able to work out what you need.