Final answer:
The probability of independent events A and B occurring simultaneously is calculated using the formula P(A) multiplied by P(B), which for independent events is P(A AND B) = P(A)P(B).
Step-by-step explanation:
If events A and B are independent, then the probability of simultaneous occurrence of event A and event B can be found with P(A)·P(B). In the context of probability theory, when two events are said to be independent, the occurrence of one event has no effect on the probability of the occurrence of the other. Therefore, to calculate the combined probability of both independent events occurring, you simply multiply their individual probabilities together, giving us the formula P(A AND B) = P(A)·P(B).
For instance, if the probability of event A occurring is 0.3 and the probability of event B occurring is 0.5, the combined probability of both A and B occurring is (0.3)·(0.5) = 0.15, which is a straightforward application of this rule. This is due to the fact that for independent events, P(B|A) = P(B) and P(A|B) = P(A), which means the conditional probability remains the same as the individual probability, indicating that one event's occurrence is not impacting the other.