Six Sigma Green Belt Certification Practice Exam

What defines mutually exclusive events?

1. Events A and B cannot occur at the same time

2. Events A and B both occur at the same time

3. All sample points not contained in event A

4. All sample points contained in event A

The correct answer is: Events A and B cannot occur at the same time

Mutually exclusive events are defined as events that cannot happen simultaneously. In the context of probability, if one event occurs, it precludes the possibility of the other event occurring at the same time. For example, when tossing a single coin, getting a 'Heads' and getting a 'Tails' are mutually exclusive events because both outcomes cannot occur together. This distinction is essential in statistical reasoning, especially when calculating probabilities, as it ensures that the outcomes are distinct. Understanding mutually exclusive events helps in setting the foundation for more complex concepts in probability and statistics, such as the addition rule for probabilities, which states that the probability of either of two mutually exclusive events occurring is the sum of their individual probabilities. The other options presented do not accurately capture the essence of mutually exclusive events. For example, stating that both events occur at the same time directly contradicts the concept. Similarly, defining mutually exclusive events based on sample points not contained in event A or those contained in event A misconstrues their independence from each other. The core principle remains that mutually exclusive events cannot coexist, making the first response the correct one.