Answer
The fraction of the incident light intensity that is transmitted is $\frac{1}{4}$
Work Step by Step
Since the light is unpolarized initially, the intensity of the light after passing through the first polarizer is $\frac{I_0}{2}$
We can use the law of Malus to determine the intensity of the light after passing through the second polarizer.
$I = \frac{I_0}{2}~cos^2(45^{\circ}) = \frac{1}{4}\times I_0$
The fraction of the incident light intensity that is transmitted is $\frac{1}{4}$
