High and low pressure area and raining It is more likely for an area with higher atmospheric pressure to be sunny. In the same way, it is more probable in low-pressure areas for it to rain.
This is because of the law which states $pV=(c)T$ where $p$ is pressure, $V$ is volume, $T$ is temperature and $(c)$ is a constant value, for the same $T$ temperature, lowering pressure $p$ should lead to increase volume of the gas (air in this example).
Ant vice versa: lowering volume $V$ leads to an increase in pressure $p$. The gas should be guided to condensation and the rain.
So using this basic formula high pressure area should be more likely to cause rain.
Where am I thinking wrong? Are there too many simplifications?
 A: Generally speaking low and high pressure areas are associated with vertical movement of the air. Air rises in a low pressure area and falls in a high pressure area. In a low pressure area the rising air cools and this is likely to condense water vapour and form clouds, and consequently rain. The opposite is true in a high pressure area, which is why high pressure tends to give cloudless skies.
However, you should also note that low pressure areas tend to be associated with weather fronts, and these (especially cold fronts) also cause rain.
A: An increase in pressure is not what causes condensation and rain.
Besides, the formula $pV = \text{const}$ applies to an isolated sample of a fixed amount of gas at a fixed temperature. Those conditions don't hold true for air in the atmosphere.
The real reason it rains is quite complicated, but the gist of it is that upward air currents can carry air with a high concentration of water vapor from near the surface into the upper atmosphere. As this happens, the air's temperature drops because of the reduced pressure and also because of heat loss to the colder surrounding air. When the air gets cool enough, the water condenses out and may fall as rain. These upward air currents produce low pressure as a side effect.
A: The atmosphere is a mixture of dry air and water vapour, where the content of the latter may vary. Water vapour is lighter than air, hence a vertical column of this gaseous mixture will weigh less (i.e. cause less pressure) when there is more water vapour.
When atmosperic temperature is constant in horizontal directions, low pressure means (is caused by) more water vapour in the atmopshere. When there is more water vapour the chance of rain is higher. Starting from here one may add the already mentioned effects of vertical rise of the air and water vapour.
A: I will make it very simple.
The low pressure air is always pushed by the surrounded High pressure air! (because air moves from HP to LP).
When this HP air pushes horizontally, the LP air moves Vertically upward.
As this air moves upward, Becomes dense and forms clouds and we get rain.
