The probability of two independent events occurring together is the product of their individual probabilities. This is known as the "product rule" or the "multiplication rule" of probability.
The probability of A or B occurring is calculated by adding the individual probabilities of A and B, and then subtracting the probability of both A and B occurring together (since this was already accounted for in the individual probabilities).
Independent events are events that do not affect each other's probabilities. For example, the outcome of a coin toss does not affect the outcome of a dice roll. Dependent events are events where the outcome of one event affects the probability of the other event. For example, drawing a red card from a deck and then drawing another card without replacing the first one would be a dependent event, as the probability of drawing a red card on the second draw would be affected by the first draw.
The sample space is the set of all possible outcomes for a given event. It is important to correctly identify the sample space in order to accurately calculate probabilities. If the sample space is not correctly identified, the probabilities may be incorrect.
Theoretical probabilities are calculated based on mathematical principles and assumptions, while experimental probabilities are determined through actual experiments or observations. Theoretical probabilities can be used to predict outcomes, while experimental probabilities are based on actual data and may be more accurate in certain situations.