With the increasing wind penetration level in power systems, transmission system operators have become concerned about frequency stability. The inertia of a variable speed wind turbine is decoupled by power electronic converters from the power network and therefore does not intrinsically contribute to power system inertia. Moreover, as wind plant progressively displaces conventional generation and their inertia, a substantial reduction in power system inertia may occur. Variable speed wind turbines can be controlled to provide synthetic inertial response to compensate for their lack of direct contribution to power system inertia. A probabilistic approach to assessing the collective inertial contributions from wind generation across a power system is proposed and is applied to the Great Britain power system. The impact of the aggregate inertial response on arresting frequency fall is examined for the case of a sudden generation loss of 1.8 GW at the time of minimum load on both a mid-summer and a midwinter day. The results show that synthetic inertial response from wind can reduce the rate of fall of frequency and the minimum system frequency (nadir) following the loss of generation event.