Answer
See below.
Work Step by Step
Suppose that the ideal Polaroid filter has its transmission axis oriented along the horizontal direction, the x-axis. Then, the filter transmits all of the light's x-components, and none of the perpendicular y-components (i.e., the vertical components).
Roughly speaking, random unpolarized light can be resolved (like a vector) into components along the x-direction, and an equal number along the y-direction. An ideal Polaroid filter lets through only the components that are parallel to its transmission axis, which is half of the incoming unpolarized light..