The probability that you are late to school is 0.05 for any day. Given that you slept late, the probability that you are late to school is 0.13. Are the events "Late to School" and "Slept Late" independent or dependent?
They are dependent .
The event "slept late" influences the probability of the other event "late to school".
An example of independent events are flipping a coin repeatedly.
Since the coin has no memory, the probabilities at the second (or later) tosses are still 50/50 -- provided it is fair coin!
You may want to think this one over:
You meet a friend, whom you have not spoken to for years. All you know is that he has two children. When you meet him, he has his son with him.
What are the chances that the other child is also a son?
(no, it's not 50/50)
If you get this, you will never worry about dependent/independent again.