What does it mean for two events to be independent in probability?

• A. The occurrence of one event affects the probability of the other
• B. Both events cannot occur at the same time
• C. The occurrence of one event does not affect the occurrence of the other
• D. The total outcomes are not equally likely

Answer: (C)

Independence in probability means that the occurrence of one event has no impact on the occurrence of another event. When two events are independent, the probability of both events happening together is simply the product of their individual probabilities. This is represented mathematically as P(A and B) = P(A) * P(B).

For instance, if you were to flip a coin and roll a die, the result of the coin flip (heads or tails) does not change the probability outcomes of the die roll (1 through 6). Therefore, knowing the outcome of the coin flip will not influence the likelihood of any number appearing on the die. This illustrates the concept of independence clearly. In contrast, if one event affects the probability of another or if both events cannot occur simultaneously, they are considered dependent events, which follows different rules.