Exponential waiting time between collisions

Consider the particle moving in a gas of other particles. Given that the last collision of the particle occurred at \(t = 0\) , the probability that the next collision will occur between t and \(t + \Delta t\) equals \(\lambda \Delta t + o ( \Delta t )\) , when \(\Delta t \to 0\) . Find the probability \(P ( t )\) that the time between the nearest collisions will exceed t.