What does it mean for two events to be independent?

What does it mean for two events to be independent?

• A. The occurrence of one event changes the probability of the other
• B. Both events can occur simultaneously with certainty
• C. The occurrence of one event does not affect the occurrence of the other
• D. Independent events cannot occur at the same time

Answer: (C)

When two events are independent, it means that the occurrence of one event does not influence the probability of the occurrence of the other event. In practical terms, this means that if you were to have one event happen, it would not change the likelihood of the other event happening. For example, if you flip a coin and roll a die, the outcome of the coin flip does not affect the outcome of the die roll. This concept is fundamental in statistics and probability, as it allows for the simplification of calculations when dealing with multiple events. If two events are independent, the probability of both events occurring is simply the product of their individual probabilities. Thus, understanding and correctly identifying independent events is crucial for solving many problems in statistics.

When two events are independent, it means that the occurrence of one event does not influence the probability of the occurrence of the other event. In practical terms, this means that if you were to have one event happen, it would not change the likelihood of the other event happening. For example, if you flip a coin and roll a die, the outcome of the coin flip does not affect the outcome of the die roll.

This concept is fundamental in statistics and probability, as it allows for the simplification of calculations when dealing with multiple events. If two events are independent, the probability of both events occurring is simply the product of their individual probabilities. Thus, understanding and correctly identifying independent events is crucial for solving many problems in statistics.