Little stuck on a Poisson problem.

I remember something about the exponential distribution being the time between Poisson processes, but not sure how to apply it here.Sightings of a particular species of rare bird occur at a rate of 6 per year. Assume that sightings can be modelled by a Poisson process $\displaystyle (N(t), t>0)$ where time $\displaystyle t$ is measured in years and time 0 is the present time.

Let $\displaystyle T_1$ be the time from time 0 until the 1st sighting. What is the probability that $\displaystyle T_1$ is at most:

i) 1.

ii) 2.

Would $\displaystyle T_1$ be distributed $\displaystyle Ex(12)$?

Thanks in advance