Problem $3$: Initially unpolarized light strikes a polarizer oriented vertically. The light transmitted by the first polarizer is then incident on a second polarizer which is oriented horizontally.

a$.$ What percent of light is transmitted by this pair of filters? Briefly explain your reasoning. $(2$ points$)$

b$.$ You now include a third filter in this arrangement with a polarization angle of $25$ from the vertical. You try placing the filter in each of the numbered positions shown in the figure $(1$: before the pair, $2$: between the pair, and $3$: after the pair$).$ What is the amount of light transmitted by each combination? Make sure to show your work$/$explain your reasoning, for full credit. $(8$ points$)$