Final answer:
The statement is false; the addition rule is used for determining the probability of either event occurring (P(A or B)), while the multiplication rule is used for the probability of both events occurring (P(A and B)).
Step-by-step explanation:
The student's statement about using the addition rule to determine the probability of the intersection of two events is false. The correct rule for finding the joint probability of two events occurring, denoted as P(A and B), is the multiplication rule. The multiplication rule states that if events A and B are defined on a sample space, the probability that both A and B occur is P(A and B) = P(A|B)P(B), assuming that event B has a non-zero probability of occurring.
For independent events, where the outcome of one event does not influence the outcome of another, the multiplication rule simplifies to P(A and B) = P(A)P(B). Conversely, the addition rule is used to determine the probability of either event A or event B occurring (denoted as P(A or B)). This rule states P(A or B) = P(A) + P(B) - P(A and B) and is applicable when you want to find the probability of at least one of the events occurring. It's important to subtract P(A and B) to avoid double-counting the probability of both events occurring.
It is also important to distinguish between independent events and mutually exclusive events. Mutually exclusive events cannot happen at the same time; thus, if events A and B are mutually exclusive, P(A and B) = 0, which affects the way the addition rule is applied.