Final answer:
Using a credit card that gives a mile for each dollar spent and charging more than $2,000 per month are independent events because the occurrence of one does not influence the probability of the other.
Step-by-step explanation:
The question you're asking centers around the concept of independent events in probability. Independent events are two or more events where the occurrence of one does not affect the probability of the occurrence of the other. In the scenario you have provided, using a credit card that gives a mile of air travel for each dollar spent and charging more than $2,000 per month are considered two separate activities.
To determine if these are independent events, ask yourself whether the probability of one event occurring impacts the other. Earning a mile for each dollar spent happens for every dollar charged to the card, regardless of the total amount spent in a month. Therefore, earning miles is not dependent on the total monthly charge. Conversely, charging more than $2,000 in a single month is a separate transactional behavior that does not influence the miles earned per dollar.
Since these two events do not impact each other's probability, charging more than $2,000 per month and earning a mile for each dollar spent are indeed independent events. This concept is essential in understanding how different factors or actions do not affect one another, which can be applied to many real-world scenarios and is valuable in decision-making.