Cars pass a certain street location according to a Poisson process with rate lambda. A woman who wants to cross the street at that location wait until she can see that no cars will come by in the next T time units. Find the probability that her waiting time is T.
The Attempt at a Solution
I know that interarrival times have an exponential distribution.
If X is the arrival of the next car,
P(waiting time = T) = P( X > T )
But I am not sure what this means. Any help would be appreciated.