Final answer:
Mutually exclusive events are those that cannot occur at the same time, with a probability of 0 if both are to happen, whereas independent events do not affect each other's probability of occurrence. These concepts are not the same, as mutually exclusive events cannot be independent.
Step-by-step explanation:
Mutually exclusive events are two or more events that cannot happen at the same time. For example, if A and B are mutually exclusive, then P(A AND B) = 0. On the other hand, two events are independent if the occurrence of one does not affect the probability of the occurrence of the other. Regarding the given probabilities, P(E|F) is not provided, but since E and F are mutually exclusive, it can only be 0, this applies to P(U AND V) as well. As for P(U|V), it would also be 0 since U and V cannot occur together. P(U OR V) can be found by adding their probabilities, which in this case would be 0.26 + 0.37 = 0.63.
Concerning the confusion between mutually exclusive and independent events, they are not the same. If two events are mutually exclusive, they cannot be independent because if one occurs, the other cannot, meaning the occurrence of one event completely rules out the occurrence of the other, thereby affecting its probability. Hence, the student's statement comparing mutually exclusive and independent events as the same is inaccurate.
Based on these definitions, we can conclude that while mutually exclusive events have no outcomes in common and cannot occur simultaneously, independent events do not influence each other's likelihood of occurring, a fundamental difference in probabilistic terms.