"In Exercises 19-22, determine whether the events are independent or dependent. Explain your reasoning.
21. Taking a driver's education course and passing the driver's license exam"

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Understand the concept of independent and dependent events: Independent events are those where the occurrence of one event does not affect the probability of the other event. Dependent events are those where the occurrence of one event does affect the probability of the other event.

Analyze the relationship between the two events: Event 1 is 'Taking a driver's education course,' and Event 2 is 'Passing the driver's license exam.'

Consider whether taking a driver's education course influences the likelihood of passing the driver's license exam. If taking the course provides knowledge or skills that increase the probability of passing the exam, the events are dependent.

If the events are dependent, explain that the outcome of Event 1 (taking the course) directly impacts the outcome of Event 2 (passing the exam). If the events are independent, explain that taking the course has no effect on the probability of passing the exam.

Conclude by stating whether the events are independent or dependent based on the reasoning provided in the previous steps.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Independent Events

Independent events are those whose outcomes do not affect each other. In probability, two events A and B are independent if the occurrence of A does not change the probability of B occurring, and vice versa. For example, flipping a coin and rolling a die are independent events because the result of one does not influence the other.

Dependent Events

Dependent events are those where the outcome of one event affects the outcome of another. In probability, two events A and B are dependent if the occurrence of A changes the probability of B occurring. For instance, drawing cards from a deck without replacement is a classic example of dependent events, as the first draw affects the composition of the deck for the second draw.

Conditional Probability

Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which represents the probability of event A occurring given that event B has occurred. Understanding conditional probability is crucial for determining whether events are independent or dependent, as it helps to analyze how the occurrence of one event influences the likelihood of another.

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