Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

Which of the following is an example of a dependent event?

1. Drawing two cards from a deck without replacement

2. Flipping a coin twice

3. Rolling two dice

4. Choosing a marble from one bag and then another bag

The correct answer is: Drawing two cards from a deck without replacement

In probability, dependent events are those where the outcome of one event influences the outcome of another. Drawing two cards from a deck without replacement is a classic example of dependent events. Once the first card is drawn, it alters the composition of the deck for the second draw. This means that the probability of drawing a specific card changes based on the outcome of the first draw, demonstrating the dependency between the two events. In contrast, events such as flipping a coin twice, rolling two dice, or choosing a marble from one bag and then another bag (where the contents of the second bag are unaffected by the outcome of the first choice) are not dependent in the same way. In these cases, the outcomes of one event do not alter the probabilities of the subsequent events. Therefore, drawing two cards without replacement is the example that best illustrates a dependent event, as it highlights the direct impact one outcome has on the next.