I'd like some help working out the probability of my model animal finding water in a day. In my 'model' there is a square landscape 17km^2 The water pool is a circle of 500m radius (so approx 0.7854km^2) So in a one off shot the chances of hitting the water is 0.7854/17 = 0.0462 right? But if I suppose that the animal can search over the course of a day, how can I incorporate this into increasing its prob. of finding the water? Assume for the sake of argument that it can travel at 1m/second and has a 500m detection range then it should 'cut out' circles the same radius as the water pool every 1000 seconds. Then I think it would cut out 86400/1000 = 86.4 in day. If this is correct how can I convert it into a probability? I know this is a ramble, but I've been at it all morning, so any help would be much appreciated!