Final answer:
The events of winning $100 on your first and second trips to a casino are classified as independent events since the outcome of one does not influence the likelihood of the other.
Step-by-step explanation:
When evaluating whether two events are independent or dependent, it is essential to assess if the occurrence of one event influences the likelihood of the other event happening. If the outcome of one event does not affect the probability of the other event, then the two are considered independent. On the other hand, if the occurrence of one event changes the probability of the other occurring, they are dependent.
The question refers to the event of winning $100 on your first trip to a casino and the event of winning $100 on your second trip. Assuming each trip to the casino is a separate event with the same odds of winning, and the previous outcomes do not influence any subsequent trip, these two events are independent events. This is analogous to rolling a fair die, where the result of one roll does not influence the result of the subsequent roll.
Therefore, for the events, 'Winning $100 on your first trip to the casino' and 'Winning $100 on your second trip to the casino', we classify these events as independent.