Draw a probability tree.
First branch up: depart on time, down, not depart on time.
Second branch following depart on time, up arrive on time and down not arrive on time.
Third branch following not depart on time, up arrive on time and down not arrive on time.
Complete the probability tree.
1. P(arrive or depart on time) = (P(arrive on time) x P(not depart on time) + (P(not arrive on time) x P(depart on time))
2. They are dependent. The fact that the plane (yes, the same plane) departure late/before due will affect the arrival time. And if you completed the probability tree correctly, you'll see that the probability that the plane does not arrive on time is different when the plane departs on time and when the plane does not.
3. The simple fact that shows that they are NOT mutually exclusive.
From a new probability tree, we see that the two events are still dependant.