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

Two events are considered independent in probability when the occurrence of one event does not impact the probability of the occurrence of the other event. This means that, mathematically, if you have two independent events A and B, the probability of both events happening together is the product of their individual probabilities: P(A and B) = P(A) * P(B).

For instance, if you flip a coin and roll a die, the result of the coin flip does not influence what number you will roll on the die. Therefore, knowing that the coin landed on heads does not change the likelihood of rolling a three on the die.

This concept is crucial in probability theory and helps in the calculation of probabilities in various situations, particularly when dealing with multiple random events happening simultaneously. Understanding independence allows one to simplify complex probability problems into manageable calculations.