Final answer:
The First Theorem of Probability, known as the Addition Rule, states that for two mutually exclusive events, the probability of either event occurring is the sum of their individual probabilities. This rule is represented mathematically as P(A OR B) = P(A) + P(B), where A and B cannot occur simultaneously. The correct option for the student's question is A.
Step-by-step explanation:
The First Theorem of Probability, often referred to as the Addition Rule or the "either/or" rule, tells us how to calculate the probability of one event or another occurring when dealing with two mutually exclusive events. If events A and B are mutually exclusive, meaning they cannot occur at the same time, the probability that either event A or event B occurs is the sum of their individual probabilities. This is expressed mathematically as P(A OR B) = P(A) + P(B).
For example, when you are flipping a penny and a quarter and want to find the probability of one coin landing on heads and one on tails, you apply the sum rule. The outcome can be achieved with either the penny showing heads and the quarter showing tails, or vice versa. Applying the sum rule, along with the multiplication rule for the individual probabilities, you get [(1/2) × (1/2)] + [(1/2) × (1/2)] = 1/2. Here, the individual coin flips are independent events, but the overall consideration of one head and one tail is a scenario involving mutually exclusive outcomes because you are looking at either/or situations.
Given the options in the question, the correct answer is: A) It tells us that if two events are mutually exclusive, the probability of either one occurring is the sum of their individual probabilities.