What does the probability formula for independent events demonstrate?

The probability formula for independent events illustrates that the probability of both events occurring simultaneously is the product of their individual probabilities. This concept is based on the premise that if two events are independent, the occurrence of one event does not affect the probability of the other event occurring.

For independent events, the formula P(a and b) = P(a) * P(b) reflects this relationship clearly. It captures the idea that to find the probability of both events a and b happening at the same time, you multiply the probabilities of each event occurring on its own.

In contrast, the other options outline different situations regarding combinations of probabilities. For example, one option describes the addition of probabilities which applies to mutually exclusive events rather than independent events. When dealing with independent events, the multiplication rule is essential for accurate calculations in probability theory. This principle is foundational in statistical analysis and is widely used in various applications, including risk assessment in industrial hygiene.