Final answer:
Mutually exclusive events have a joint probability of zero. Conditional probability in this context is also zero, but it does not imply that events are independent; on the contrary, mutually exclusive events cannot be independent since the occurrence of one excludes the other.
Step-by-step explanation:
When events A and B are mutually exclusive, this implies that the probability of A and B occurring together (P(A ∩ B)) is 0. Therefore, (a) P(A ∩ B) = 0. For part (b), the conditional probability P(A | B), which is the probability of A happening given that B has occurred, is also 0, since A and B cannot occur together. (c) P(A | B) is not equal to P(A); however, this does not apropos of their dependency - A and B are not independent by definition because being mutually exclusive violates the condition for independence; two events are independent if the occurrence of one event does not affect the probability of the other. Consequently, P(A | B) ≠ P(A) for independent events, but for mutually exclusive events, this inequality holds because P(A | B) = 0. (d) The student's statement is inaccurate; mutually exclusive events and independent events are fundamentally different. If events are mutually exclusive they cannot be independent, since the occurrence of one precludes the occurrence of the other. (e) In general, while both mutually exclusive and independent events deal with probabilities, they describe distinct relationships; mutually exclusive events cannot occur simultaneously, while independent events occur without influencing each other's probabilities.