A geography student is studying the distribution of telephone boxes in a large rural area where there is an average of 300 boxes per 500 km. A map of part of the area is divided into 50 squares, each of area 1 km2, and the student wishes to model the number of telephone boxes. per square.

(a) Suggest a suitable simple model the student could use and specify any parameters required. One of the squares is picked at random.

(b) Find the probability that this square does not contain any telephone boxes.

(c) Find the probability that this square contains at least three telephone boxes. The student suggests using this model on another map of a large city and surrounding villages.

(d) Comment, giving your reason briefly, on the suitability of the model in this situation. (L)