3.3.4 problem 41

Let $X$ be the event that Tom woke up at $8$ in the morning. Let $Y$ be the event that Tom has blue eyes. Let $Z$ be the event that Tom made it to his $7$ a.m. class.

Clearly Tom’s eye color is independent of the time he woke up and whether he made it to his early morning class or not. However, if Tom woke up at $8$, then he definitely did not make it to his $7$ am class.