How much precipitation is there in high pressure?
Depends on the situation. In most cases, high pressure means little or no precipitation. However, sometimes afternoon heating can cause stray thunderstorms to develop even under high pressure. There’s also an “overrunning” factor in which low pressure or a trough in the upper atmosphere can cause warmer air to move on top of a cool high pressure that’s at ground level. That can cause precipitation to develop in areas of very high surface air pressure.