The first thing to remember about a Low pressure system is that warm moist air is sucked into an area of lower air pressure and the whole system turns counter-clockwise in the northern hemisphere. A hurricane is a huge Low pressure system. So, hurricanes are wet and stormy. Because the air is warm and somewhat moist at the ground level where it is pulled into the low pressure system and rising with a low pressure system, moisture will condense out of the air aloft and form precipitation in the form of rain, snow, sleet, and hail.
Low pressure systems tend to bring rain in the form of cold fronts on the south western edge or warm fronts on the north eastern edge of the "eye" of the Low pressure system.