4 Probability of detection

For OTs brighter than the limit magnitude the probability of detection depends only on the fraction of the overall field of view of size of the $\gamma$-ray satellite monitored by the optical telescope during the transient event. With the assumed parameters for the telescope and typical duration of GRBs and $20^{\circ}$ size of the field the probability P is

$$P = 0.12 \cdot \left ({\frac{L} {20{^\circ}}} \right)^{-2} \... ...m s}} \right) \cdot \left (\frac{t_l}{1~{\rm s}} \right)^{-1},$$ (3)

where T is the GRB duration and t_l is the telescope scanning time of the field l.