Spatial querying

Hi,

I have a bedrock geology polygon layer and overlaying this layer I have a polygon grid consisting of 1km x 1km grid squares. I need to join the predominant bedrock geology for each individual square to that grid square. So for example, I need something like
If bedrock type 1>50% (for that square), then assign it that bedrock type. Does anyone know of a way of doing this?

Thanks